Liu Lanzhe
In this paper, we obtain the continuity for some multilinear operators related to certain non-convolution operators on the Triebel--Lizorkin space. The operators include Littlewood--Paley operator and Marcinkiewicz operator.
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We prove an inequality of Hardy type for functions in Triebel-Lizorkin spaces. The distance involved is being measured to a given Ahlfors d-regular set in R^n, with n-1<d<n. As an application of the Hardy inequality, we consider boundedness of pointwise multiplication operators, and extension problems.
Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity
本文研究双Lipschitz变量替换下Triebel-Lizorkin正则性的稳定性及逆函数正则性，通过给出均匀域上分数光滑Triebel-Lizorkin空间的等价范数（基于末阶弱导数球平均一阶差分）获得结果。
In this paper, the authors construct some counterexamples to show that the generalized Carleson measure space and the Triebel-Lizorkin-type space are not equivalent for certain parameters, which was claimed to be true in [Taiwanese J. Math. 15 (2011), 919-926]. Moreover, the authors show that for some special parameters, the generalized Carleson measure space, the Triebel-Lizorkin-type space and the Besov-type space coincide with certain Triebel-Lizorkin space, which answers a question posed in Remark 6.11(i) of [Lecture Notes in Mathematics 2005, Springer-Verlag, Berlin, 2010, xi+281 pp.].
In this work we give some maximal inequalities in Triebel-Lizorkin spaces, which are "$\dot{F}_{\infty}^{s,q}$-variants" of Fefferman-Stein vector-valued maximal inequality and Peetre's maximal inequality. We will give some applications of the new maximal inequalities and discuss sharpness of some results.
In this paper we will give a simple stopping time proof in the $\mathbb{R}^d$ setting of the matrix weighted Triebel-Lizorkin bounds proved by F. Nazarov/S. Treil and A. Volberg, respectively. Furthermore, we provide explicit matrix A${}_p$ characteristic dependence and also discuss some interesting open questions.
We prove one generalization of the Littlewood--Paley characterization of the $\mathrm{BMO}$ space where the dilations of a Schwartz function are replaced by a family of functions with suitable conditions imposed on them. We also prove that a certain family of Triebel--Lizorkin spaces can be characterized in a similar way.
In this paper, we obtain the sharp conditions of the inclusion relations between modulation spaces $M_{p,q}^s$ and Triebel-Lizorkin spaces $F_{p,r}$ for $p\leq 1$, which greatly improve and extend the results for the embedding relations between local Hardy spaces and modulation spaces obtained by Kobayashi, Miyachi and Tomita in [Studia Math. 192 (2009), 79-96].
Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $\Rd$ with weights $\W(x)= (1-|x|^2)^{μ-1/2}$, $μ\ge 0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial elements (needlets) $\{ϕ_ξ\}$, $\{ψ_ξ\}$ and it is shown that the membership of a distribution to the weighted Triebel-Lizorkin or Besov spaces can be determined by the size of the needlet coefficients $\{\ip{f,ϕ_ξ}\}$ in appropriate sequence spaces.
In a previous paper two of the authors introduced and study Gaussian Besov-Lipschitz spaces $B_{p,q}^α(γ_{d})$ and Gaussian Triebel-Lizorkin spaces $F_{p,q}^α(γ_{d})$. Now, in this paper we introduce the variable Gaussian Besov-Lipschitz spaces $B_{p(\cdot),q(\cdot)}^α(γ_{d})$ and the variable Gaussian Triebel-Lizorkin spaces $F_{p(\cdot),q(\cdot)}^α(γ_{d}),$ that is to say, Gaussian Besov-Lipschitz and Triebel-Lizorkin spaces with variable exponents, under certain additional regularity conditions on the exponents $p(\cdot)$ and $q(\cdot)$ introduced by Dalmasso and Scotto. Trivially, they inc…
Homogeneous Besov and Triebel-Lizorkin spaces associated with multi-dimensional Laguerre function expansions of Hermite type with index $α\in [-1/2,\infty)^d\backslash (-1/2,1/2)^d$, $d\geq 1$, are defined and investigated. To achieve expected goals Schwartz type spaces on $R^d_+$ are introduced and then tempered type distributions are constructed. Also, ideas from a recent paper of Bui and Duong on Besov and Triebel-Lizorkin spaces associated with Hermite functions expansions are used. This means, in particular, using molecular decomposition and an appropriate form of a Calderón reproducing f…
The Littlewood-Paley theory is extended to weighted spaces of distributions on $[-1,1]$ with Jacobi weights $ \w(t)=(1-t)^α(1+t)^β. $ Almost exponentially localized polynomial elements (needlets) $\{ϕ_ξ\}$, $\{ψ_ξ\}$ are constructed and, in complete analogy with the classical case on $\RR^n$, it is shown that weighted Triebel-Lizorkin and Besov spaces can be characterized by the size of the needlet coefficients $\{\ip{f,ϕ_ξ}\}$ in respective sequence spaces.
In a previous paper the boundedness properties of Riesz Potentials, Bessel potentials and Fractional Derivatives were studied in detail on Gaussian Besov-Lipschitz spaces $B_{p,q}^α(γ_d)$. In this paper we will continue our study proving the boundedness of those operators on Gaussian Triebel-Lizorkin spaces $F_{p,q}^α(γ_d)$. Also these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups.
Let $(M,ρ,μ)$ be a metric measure space satisfying the doubling, reverse doubling and non-collapsing conditions, and $\mathscr{L}$ be a self-adjoint operator on $L^2 (M, dμ)$ whose heat kernel $p_t (x,y)$ satisfy the small-time Gaussian upper bound, Hölder continuity and Markov property. In this paper, we give characterizations of inhomogeneous "classical" and "non-classical" Besov and Triebel-Lizorkin spaces associated to $\mathscr{L}$ in terms of continuous Littlewood-Paley and Lusin area functions defined by the heat semigroup, for complete range of indices. This extends related classical r…
In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space $F^s_{p,q}(Ω)$ in terms of first-order differences in a uniform domain $Ω$. The characterization is valid for any positive, non-integer real smoothness $s\in \mathbb{R}_+\setminus \mathbb{N}$ and {indices $1\leq p<\infty$, $1\leq q \leq \infty$} as long as the fractional part $\{s\}$ is greater than $d/p-d/q$.
In this paper we prove a parabolic Triebel-Lizorkin space estimate for the operator given by \[T^αf(t,x) = \int_0^t \int_{{\mathbb R}^d} P^α(t-s,x-y)f(s,y) dyds,\] where the kernel is \[P^α(t,x) = \int_{{\mathbb R}^d} e^{2πix\cdotξ} e^{-t|ξ|^α} dξ.\] The operator $T^α$ maps from $L^{p}F_{s}^{p,q}$ to $L^{p}F_{s+α/p}^{p,q}$ continuously. It has an application to a class of stochastic integro-differential equations of the type $du = -(-Δ)^{α/2} u dt + f dX_t$.
This paper provides equivalence characterizations of homogeneous Triebel-Lizorkin and Besov-Lipschitz spaces, denoted by $\dot{F}^s_{p,q}(\mathbb{R}^n)$ and $\dot{B}^s_{p,q}(\mathbb{R}^n)$ respectively, in terms of maximal functions of the mean values of iterated difference. It also furnishes the reader with inequalities in $\dot{F}^s_{p,q}(\mathbb{R}^n)$ in terms of iterated difference and in terms of iterated difference along coordinate axes. The corresponding inequalities in $\dot{B}^s_{p,q}(\mathbb{R}^n)$ in terms of iterated difference and in terms of iterated difference along coordinate …
Triebel-Lizorkin spaces in Dunkl setting
本文在有限反射群相关的 Dunkl 背景下建立了 Triebel-Lizorkin 空间，利用 L^2 空间、Dunkl-Calderon-Zygmund 奇异积分算子、新重现公式及小波型与原子分解作为核心工具。
Bilinear and Fractional Leibniz Rules Beyond Euclidean Spaces: Weighted Besov and Triebel--Lizorkin Estimates
本文提出了一种适用于非欧几里得空间的双线性与分数勒贝格法则框架，扩展了经典Kato-Ponce不等式，并在加权空间中建立了新的估计方法。
We prove inequalities of Hardy type for functions in Triebel-Lizorkin spaces $F^s_{pq}(G)$ on a domain $G\subset\mathbb{R}^n$, whose boundary has the Aikawa dimension strictly less than $n-sp$.
On a metric measure space satisfying the doubling property, we establish several optimal characterizations of Besov and Triebel-Lizorkin spaces, including a pointwise characterization. Moreover, we discuss their (non)triviality under a Poincaré inequality.
We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class $A_\infty$. The main tool is a discretization in terms of an almost orthogonal wavelet expansion adapted to the radial situation.
In this paper, we establish the equivalence between the Hajłasz-Sobolev spaces or classical Triebel-Lizorkin spaces and a class of grand Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when $p\in(n/(n+1),\infty)$, we give a new characterization of the Hajłasz-Sobolev spaces $\dot M^{1, p}({\mathbb R}^n)$ via a grand Littlewood-Paley function.
Classifying Triebel-Lizorkin capacities in metric spaces
本文研究度量测度空间中的非局部容量，厘清三类 Triebel-Lizorkin 容量与 Riesz 容量的关系，并据此给出 Hajlasz-Triebel-Lizorkin 容量密度条件的刻画。
A pair of dual frames with almost exponentially localized elements (needlets) are constructed on $\RR_+^d$ based on Laguerre functions. It is shown that the Triebel-Lizorkin and Besov spaces induced by Laguerre expansions can be characterized in terms of respective sequence spaces that involve the needlet coefficients.
In this paper we study sharp generalizations of $\dot{F}_p^{0,q}$ multiplier theorem of Mikhlin-Hörmander type. The class of multipliers that we consider involves Herz spaces $K_u^{s,t}$. Plancherel's theorem proves $\widehat{L_s^2}=K_2^{s,2}$ and we study the optimal triple $(u,t,s)$ for which $\sup_{k\in\mathbb{Z}}{\big\Vert \big( m(2^k\cdot)φ\big)^{\vee}\big\Vert_{K_u^{s,t}}}<\infty$ implies $\dot{F}_p^{0,q}$ boundedness of multiplier operator $T_m$ where $φ$ is a cutoff function. Our result also covers the $BMO$-type space $\dot{F}_{\infty}^{0,q}$.
Characterizations of weighted Besov and Triebel-Lizorkin spaces with variable smoothness
本文研究了具有可变光滑度的加权Besov和Triebel-Lizorkin空间的等价性，并给出了时间分数演化方程的加权正则性估计和广义Sobolev嵌入定理。
Classification of anisotropic local Hardy spaces and inhomogeneous Triebel-Lizorkin spaces
本文通过拟范数的粗等价性刻画了膨胀矩阵产生相同各向异性局部Hardy和非齐次Triebel-Lizorkin空间的条件，完成了相关空间的分类。
An RD-space $\mathcal X$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in $\mathcal X$. In this paper, the authors first give several equivalent characterizations of RD-spaces and show that the definitions of spaces of test functions on $\mathcal X$ are independent of the choice of the regularity $ε\in (0,1)$; as a result of this, the Besov and Triebel-Lizorkin spaces on $\mathcal X$ are also independent of the choice of the underlying distribution space. Then the authors characterize the norms of inhomogene…
A sufficient condition for Haar multipliers in Triebel-Lizorkin spaces
针对 Haar 系统非无条件的 Triebel-Lizorkin 空间，本文研究仅依赖 Haar 频率的乘子，用变差范数给出算子有界的充分条件，并证明其在 $p,q>1$ 时关于参数 $u$ 基本最优。
In this note, we establish characterizations for the homogeneous Besov-type spaces $\dot{B}^{s,τ}_{p,q}(\mathbb{R}^n)$ and Triebel-Lizorkin-type spaces $\dot{F}^{s,τ}_{p,q}(\mathbb{R}^n)$, introduced by Yang and Yuan, through fractional Hajłasz-type gradients for suitable values of the parameters $p$, $q$ and $τ$ when $0 < s < 1$, and through grand Littlewood-Paley-type maximal functions for all admissible values of the parameters. These characterizations extend the characterizations obtained by Koskela, Yang and Zhou for the standard homogeneous Besov and Triebel-Lizorkin spaces.
Hardy spaces, Besov spaces and Triebel--Lizorkin spaces associated with a discrete Laplacian and applications
本文针对整数集上的离散拉普拉斯算子$Δ_d$定义了相关Hardy、Besov及Triebel--Lizorkin空间，证明其与经典空间一致，并应用于谱乘子和Riesz变换的有界性证明。
On matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces
本文研究了矩阵加权Bourgain-Morrey Triebel-Lizorkin空间的定义、等价范数及特征描述，并探讨了伪微分算子在该空间上的有界性。
Pseudo-differential operators of type $(1,1)$ and order $m$ are continuous from $F_p^{s+m,q}$ to $F_p^{s,q}$ if $s>d/\min{(1,p,q)}-d$ for $0<p<\infty$, and from $B_p^{s+m,q}$ to $B_{p}^{s,q}$ if $s>d/\min{(1,p)}-d$ for $0<p\leq\infty$. In this work we extend the $F$-boundedness result to $p=\infty$. Additionally, we prove that the operators map $F_{\infty}^{m,1}$ into $bmo$ when $s=0$, and consider Hörmander's twisted diagonal condition for arbitrary $s\in\mathbb{R}$. We also prove that the restrictions on $s$ are necessary conditions for the boundedness to hold.
In this article, the authors establish the pointwise characterization of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type via clarifying the relationship among Hajłasz-Sobolev spaces, Hajłasz-Besov and Hajłasz-Triebel-Lizorkin spaces, grand Besov and Triebel-Lizorkin spaces, and Besov and Triebel-Lizorkin spaces. A major novelty of this article is that all results presented in this article get rid of both the dependence on the reverse doubling condition of the measure and the metric condition of the quasi-metric under consideration. Moreover, the pointwise characterization of th…
In this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the outcome belongs to the scale of the so-called diamond spaces.
Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calderón--Zygmund Operators
研究利用分子与小波刻画，证明伪微分、迹及 Calderón–Zygmund 算子在矩阵 $\mathcal{A}_{\infty}$ 权广义 Besov–Triebel–Lizorkin 型空间上的有界性。
We give a new characterization of (homogeneous) Triebel-Lizorkin spaces $\dot{\mathcal F}^{s}_{p,q}(Z)$ in the smoothness range $0 < s < 1$ for a fairly general class of metric measure spaces $Z$. The characterization uses Gromov hyperbolic fillings of $Z$. This gives a short proof of the quasisymmetric invariance of these spaces in case $Z$ is $Q$-Ahlfors regular and $sp = Q > 1$. We also obtain first results on complex interpolation for these spaces in the framework of doubling metric measure spaces.
In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Hajłasz-Triebel-Lizorkin and Hajłasz-Besov spaces in the general context of quasi-metric measure spaces for an optimal range of the smoothness parameter $s$. An interesting facet of this work is how the range of $s$ for which the above characterizations of these embeddings hold true is intimately linked (in a quantitative manner) to the geometric makeup of the underlying space. Moreover, although stated for Hajłasz-Triebel-Lizorkin and…
Triebel-Lizorkin spaces and expansive matrices
本文探讨了扩张矩阵生成相同各向异性齐次Triebel-Lizorkin函数空间或序列空间的分类定理，分析了函数空间与序列空间在等价条件上的差异。
Continuing previous work, this paper provides maximal characterizations of anisotropic Triebel-Lizorkin spaces $\dot{\mathbf{F}}^α_{p,q}$ for the endpoint case of $p = \infty$ and the full scale of parameters $α\in \mathbb{R}$ and $q \in (0,\infty]$. In particular, a Peetre-type characterization of the anisotropic Besov space $\dot{\mathbf{B}}^α_{\infty,\infty} = \dot{\mathbf{F}}^α_{\infty,\infty}$ is obtained. As a consequence, it is shown that there exist dual molecular frames and Riesz sequences in $\dot{\mathbf{F}}^α_{\infty,q}$.
We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces $Z$. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices $s<1,$ as well as the first order Hajłasz-Sobolev space $M^{1,p}(Z)$. They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset $F \subset Z$ are Besov spaces defined intrinsically on $F$. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.
Let $(M, ρ,μ)$ be an RD-space satisfying the non-collapsing condition. In this paper, the authors introduce Besov-type spaces $B_{p,q}^{s,τ}(M)$ and Triebel--Lizorkin-type spaces $F_{p,q}^{s,τ}(M)$ associated to a non-negative self-adjoint operator $L$ whose heat kernels satisfy some Gaussian upper bound estimate, Hölder continuity, and the stochastic completeness property. Characterizations of these spaces via Peetre maximal functions and heat kernels are established for full range of indices. Also, frame characterizations of these spaces are given. When $L$ is the Laplacian operator on $\mat…
We characterize the Schauder and unconditional basis properties for the Haar system in the Triebel-Lizorkin spaces $F^s_{p,q}(\Bbb R^d)$, at the endpoint cases $s=1$, $s=d/p-d$ and $p=\infty$. Together with the earlier results in [10], [4], this completes the picture for such properties in the Triebel-Lizorkin scale, and complements a similar study for the Besov spaces given in [5].
In this article, the authors establish the wavelet characterization of Besov and Triebel--Lizorkin spaces on a given space $(X,d,μ)$ of homogeneous type in the sense of Coifman and Weiss. Moreover, the authors introduce almost diagonal operators on Besov and Triebel--Lizorkin sequence spaces on $X$, and obtain their boundedness. Using this wavelet characterization and this boundedness of almost diagonal operators, the authors obtain the molecular characterization of Besov and Triebel--Lizorkin spaces. Applying this molecular characterization, the authors further establish the Littlewood--Paley…
In this paper we define Besov-Lipschitz and Triebel-Lizorkin spaces in the context of Gaussian harmonic analysis, the harmonic analysis of Hermite polynomial expansions. We study inclusion relations among them, some interpolation results and continuity results of some important operators (the Ornstein-Uhlenbeck and the Poisson-Hermite semigroups and the Bessel potentials) on them. We also prove that the Gaussian Sobolev spaces $L^p_α(γ_d)$ are contained in them. The proofs are general enough to allow extensions of these results to the case of Laguerre or Jacobi expansions and even further in t…
Weighted Bourgain-Morrey-Besov type and Triebel-Lizorkin type spaces associated with operators
本文在齐次型空间上，针对非负自伴算子引入加权Bourgain-Morrey-Besov型与Triebel-Lizorkin型空间，给出连续刻画、原子分子分解，并证明分数幂与谱乘子的有界性。
Let $\ell\in\mathbb{N}$ and $p\in(1,\infty]$. In this article, the authors prove that the sequence $\{f-B_{\ell,2^{-k}}f\}_{k\in\mathbb{Z}}$ consisting of the differences between $f$ and the ball average $B_{\ell,2^{-k}}f$ characterizes the Besov space $\dot B^α_{p,q}(\rn)$ with $q\in (0, \infty]$ and the Triebel-Lizorkin space $\dot F^α_{p,q}(\rn)$ with $q\in (1,\infty]$ when the smoothness order $α\in(0,2\ell)$. More precisely, it is proved that $f-B_{\ell,2^{-k}}f$ plays the same role as the approximation to the identity $φ_{2^{-k}}\ast f$ appearing in the definitions of $\dot B^α_{p,q}(\rn…
Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale
本文研究平面区域上拟共形映射在Sobolev、Bessel位势和Triebel-Lizorkin尺度下的全局正则性，利用边界几何和Beltrami系数光滑性建立最优条件，并证明在光滑性低于1的Triebel-Lizorkin类中该条件同样保证主解的全局正则性。
Regularity of Characteristic Functions in Besov-Type and Triebel--Lizorkin-Type Spaces
本文在边界δ邻域测度受限的条件下，确定了Besov型与Triebel--Lizorkin型空间中特征函数的最优正则性，并得到雪花域和螺旋型域特征函数属于这些空间的充要条件。
Discrete Triebel-Lizorkin spaces and expansive matrices
本文研究了扩张矩阵产生相等离散各向异性Triebel-Lizorkin空间的条件，扩展了Triebel关于对角扩张的结果。
Let $α\in\mathbb R$, $q\in(0,\infty]$, $p\in(0,\infty)$, and $W$ be an $A_p(\mathbb{R}^n,\mathbb{C}^m)$-matrix weight. In this article, the authors characterize the matrix-weighted Triebel-Lizorkin space $\dot{F}_{p}^{α,q}(W)$ via the Peetre maximal function, the Lusin area function, and the Littlewood-Paley $g_λ^{*}$-function. As applications, the authors establish the boundedness of Fourier multipliers on matrix-weighted Triebel-Lizorkin spaces under the generalized Hörmander condition. The main novelty of these results exists in that their proofs need to fully use both the doubling property…
A coherent theory of tent spaces and homogeneous Triebel-Lizorkin spaces
本文提出并系统研究了一类帐篷空间，用于刻画同质Triebel-Lizorkin空间˙F^β_{p,q}，并将其与经典Coifman、Meyer和Stein空间进行比较，同时与Huang发展的加权帐篷空间等价，进一步提供了端点空间˙F^β_{∞,q}的新刻画。
On a general Lie group $G$ endowed with a sub-Riemannian structure and of local dimension $d$, we characterize the pointwise multipliers of Triebel--Lizorkin spaces $F^{p,q}_α$ for $p,q\in (1,\infty)$ and $α>d/p$, and those of Besov spaces $B^{p,q}_α$ for $q\in [1,\infty]$, $p>d$ and $d/p< α<1$. When $G$ is stratified, we extend the latter characterization to all $p,q\in [1,\infty]$ and $α>d/p$.
In this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the Lebesgue spaces $L^p(\Rdst)$, $1<p<+\infty$. The novelty and difficulty of this construction is that we allow for non-lattice translations. We prove that for an arbitrary expansive matrix $A$ and any set $Λ$ - satisfying a certain spreadness condition but otherwise irregular- there exists a smooth window whose translations along the elements of $Λ$ and dilations by powers of $A$ provide an atomic decomposition for the whole range of the anisotropic Tr…
In this article, the authors introduce Besov and Triebel-Lizorkin spaces on spaces of homogeneous type in the sense of Coifman and Weiss, prove that these (in)homogeneous Besov and Triebel-Lizorkin spaces are independent of the choices of both exp-ATIs (or exp-IATIs) and underlying spaces of distributions, and give some basic properties of these spaces. As applications, the authors show that some known function spaces coincide with certain special cases of Besov and Triebel-Lizorkin spaces and, moreover, obtain the boundedness of Calderón-Zygmund operators on these Besov and Triebel-Lizorkin s…
In this article, the authors first introduce the Triebel-Lizorkin-type space $F_{p(\cdot),q(\cdot)}^{s(\cdot),ϕ}(\mathbb R^n)$ with variable exponents, and establish its $φ$-transform characterization in the sense of Frazier and Jawerth, which further implies that this new scale of function spaces is well defined. The smooth molecular and the smooth atomic characterizations of $F_{p(\cdot),q(\cdot)}^{s(\cdot),ϕ}(\mathbb R^n)$ are also obtained, which are used to prove a trace theorem of $F_{p(\cdot),q(\cdot)}^{s(\cdot),ϕ}(\mathbb R^n)$. The authors also characterize the space $F_{p(\cdot),q(\c…
Preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with operators
研究齐次型空间上与算子相关的加权齐次Bourgain-Morrey Besov-Triebel-Lizorkin空间的预对偶，引入块空间并证明其与单位分解选择无关。
We obtain new molecular decompositions and molecular synthesis estimates for Hermite Besov and Hermite Triebel--Lizorkin spaces and use such tools to prove boundedness properties of Hermite pseudo-multipliers on those spaces. The notion of molecule we develop leads to boundedness of pseudo-multipliers associated to symbols of Hörmander-type adapted to the Hermite setting on spaces with non-positive smoothness; in particular, we obtain continuity results for such operators on Lebesgue and Hermite local Hardy spaces. As a byproduct of our results on boundedness properties of pseudo-multipliers, …
This paper provides maximal function characterizations of anisotropic Triebel-Lizorkin spaces associated to general expansive matrices for the full range of parameters $p \in (0,\infty)$, $q \in (0,\infty]$ and $α\in \mathbb{R}$. The equivalent norm is defined in terms of the decay of wavelet coefficients, quantified by a Peetre-type space over a one-parameter dilation group. As an application, the existence of dual molecular frames and Riesz sequences is obtained; the wavelet systems are generated by translations and anisotropic dilations of a single function, where neither the translation no…
A Battle-Lemarié Frame Characterization of Besov and Triebel-Lizorkin Spaces
本文研究了由过采样生成的样条框架与Battle-Lemarié小波系统的非负整数阶关系，建立了光滑参数至s < n+1的Besov和Triebel-Lizorkin（准）范数刻画，并证明了端点情况s=n+1的结果。
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