Zhuang Wang
In this paper, we study the traces of Orlicz-Sobolev spaces on a regular rooted tree. After giving a dyadic decomposition of the boundary of the regular tree, we present a characterization on the trace spaces of those first order Orlicz-Sobolev spaces whose Young function is of the form $t^p\log^λ(e+t)$, based on integral averages on dyadic elements of the dyadic decomposition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces.
We study trace inequalities of the type $$ \| T_k f\|_{L^q(dμ)}\leq C \|f\|_{L^p(dσ)}, \qquad f \in L^p(dσ), $$ in the ``upper triangle case'' $1 \leq q<p$ for integral operators $T_k$ with positive kernels, where $dσ$ and $dμ$ are positive Borel measures on $\R^n$. Our main tool is a generalization of Th. Wolff's inequality which gives two-sided estimates of the energy ${\mathcal E}_{k, σ} [μ]=\int_{\R^n} (T_k [μ])^{p'} d σ$ through the $L^1(dμ)$-norm of an appropriate nonlinear potential $W_{k, σ}[μ]$ associated with the kernel $k$ and measures $dμ$, $d σ$. We initially work with a dyadic in…
We prove that the $\cal P$ norm estimate between a Hardy martingale and its cosine part are stable under dyadic perturbations, and show how dyadic stability of the $\cal P$ norm estimate is used in the proof that $L^1$ embeds into $L^1/H^1$.
The dyadic paraproduct is bounded in weighted Lebesgue spaces $L_p(w)$ if and only if the weight $w$ belongs to the Muckenhoupt class $A_p^d$. However, the sharp bounds on the norm of the dyadic paraproduct are not known even in the simplest $L_2(w)$ case. In this paper we prove the linear bound on the norm of the dyadic paraproduct in the weighted Lebesgue space $L_2(w)$ using Bellman function techniques and extrapolate this result to the $L_p(w)$ case.
We obtain sharp estimates for the quasi norm of the maximal function of f when it satisfies certain conditions.
A Dyadic Approach to Weak Characterizations of Function Spaces
本文利用二进立方体上的平均振荡或均值定义弱型拟范数，将其作为上半空间相应拟范数的离散变体，通过与已知函数空间比较，获得了新嵌入与刻画，并举例证明了结果的精确性。
In this paper we show how to compute the $Λ_α$ norm, $α\ge 0$, using the dyadic grid. This result is a consequence of the description of the Hardy spaces $H^p(R^N)$ in terms of dyadic and special atoms.
We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions $B$ which define a bounded paraproduct on $L^2(H)$. We obtain several equivalent formulations of $\|π_B\|$ in terms of the norm of the "sweep" function of $B$ or of averages of the norms of martingales transforms of $B$ in related spaces. Furthermore, we investigate a connection between John-Nirenberg type inequalities and Carleson-type inequalities via a product formula for paraproducts and deduce sharp dimensional estimates for John-Nirenberg type inequalities.
We show that if the Hilbert transform with values in a Banach space is $L^p$ bounded, then so is the dyadic Hilbert transform, with a linear relation of the norms.
In this paper, we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases. We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces, and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces (on hyperplanes) which are defined by using integral averages over selected layers of dyadic cubes.
We prove continuity and surjectivity of the trace map onto $L_p$, from a space of functions of locally bounded variation, defined by the Carleson functional. The extension map is constructed through a stopping time argument. This extends earlier work by Varopoulos in the BMO case, related to the Corona theorem. We also prove $L_p$ Carleson approximability results for solutions to elliptic non-smooth divergence form equations, which generalize results in the case $p=\infty$ by Hofmann, Kenig, Mayboroda and Pipher.
We give necessary and sufficient conditions in order that inequalities of the type $$ \| T_K f\|_{L^q(dμ)}\leq C \|f\|_{L^p(dσ)}, \qquad f \in L^p(dσ), $$ hold for a class of integral operators $T_K f(x) = \int_{R^n} K(x, y) f(y) d σ(y)$ with nonnegative kernels, and measures $d μ$ and $dσ$ on $\R^n$, in the case where $p>q>0$ and $p>1$. An important model is provided by the dyadic integral operator with kernel $K_{\mathcal D}(x, y) \sum_{Q\in{\mathcal D}} K(Q) χ_Q(x) χ_Q(y)$, where $\mathcal D=\{Q\}$ is the family of all dyadic cubes in $\R^n$, and $K(Q)$ are arbitrary nonnegative constants a…
The Operator Norm of Paraproducts on Hardy Spaces
本文研究了广义算子在Hardy空间上的算子范数，证明了其与分布的范数关系，并扩展到dyadic Hardy空间。
Structural Properties of the Köthe Dual of the Matricial Bloch Space
研究矩阵布洛赫空间的Köthe对偶$\mathcal{B}(D,\ell_2)^K$，反驳其与特定空间一致的猜想，揭示对对角线元素位置敏感，通过托普利兹矩阵测试恢复迹范数变体，建立行向、列向及迹范数条件的双边估计。
Extensions of traces for Sobolev mappings into manifolds at the endpoint $p=1$
该研究针对边界紧的黎曼流形到完备黎曼流形的$W^{1,1}$型Sobolev映射，通过二进立方体格铺砌定义域的方法构造延拓，直接证明了迹与延拓定理，还得到了映射$L^1$能量的渐近刻画，结果可推广至半空间与带状区域。
Haar frame characterizations of Besov-Sobolev spaces and optimal embeddings into their dyadic counterparts
本文研究了非无条件基参数下Besov和Triebel-Lizorkin空间的Haar系数行为，利用双重过采样Haar框架刻画了这些空间，并证明了经典空间与其二进对应空间之间的闭子集关系及端点情形下的等价范数。
The Operator Norm of Paraproducts on Bi-parameter Hardy spaces
本文研究了双参数Hardy空间上二进仿积算子的算子范数，证明了其范数与符号函数在相应Hardy空间或BMO空间中的范数等价，并将结果推广到双参数Fourier仿积算子。
Weighted composition--differentiation operators on mixed-norm, derivative Hardy and F(p,q,s) spaces
该研究探讨混合范数、导数Hardy空间与F(p,q,s)空间上的加权复合微分算子，通过二进准则得到其有界性等性质，还获乘子、Schatten准则及精确奇异值等结果。
The Kerman-Sawyer trace theorem for product Morrey spaces
通过并行圆冠分解，将Kerman-Sawyer迹不等式从Lebesgue空间扩展到乘积Morrey空间，提出新的分析工具和方法。
Distance and best approximations in operator norm and trace class norm
该研究针对算子空间与迹类算子空间的最佳逼近及距离问题，推导了两类空间的距离表达式，拓展至有限维C*-代数情形，且通过实例验证了结果的计算优势。
We prove that the operator norm of every Banach space valued Calderon-Zygmund operator T on the weighted Lebesgue-Bochner space depends linearly on the Muckenhoupt A_2 characteristic of the weight. In parallel with the proof of the real-valued case, the proof is based on pointwise dominating every Banach space valued Calderon-Zygmund operator by a series of positive dyadic shifts. In common with the real-valued case, the pointwise dyadic domination relies on Lerner's local oscillation decomposition formula, which we extend from real-valued functions to Banach space valued functions. The extens…
Vector-Carleson, Calderón, and Poisson-Atomic Criteria for Generalized Hilbert Operators on $H^p$, $p>2$
该研究针对p>2时广义希尔伯特算子在H^p上的有界性，建立了向量卡尔松等判据，构造了特殊符号并证明泊松原子检验定理，给出原子复杂度公式与检验界。
Embedded trace operator for infinite metric trees
本文研究无限加权度量树上的迹算子，统一了两种已有的边界迹构造，证明其等价性，并建立迹的Sobolev正则性，同时提出与任意紧致黎曼流形的等同方法。
We study non-linear traces of Choquet type and Sugeno type on matrix algebras. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both Choquet type and Sugeno type respectively. There exists a close relation among non-linear traces of Choquet type, majorization, unitary invariant norms and 2-positivity.
We introduce the fundamental group $F(\mathcal{M})$ of a finite von Neumann algebra $\mathcal{M}$ with finite dimensional normal trace space. The form of $F(\mathcal{M})$ is completely determined. Moreover, there exists a finite von Neumann algebra $\mathcal{M}$ with finite dimensional normal trace space such that $F(\mathcal{M})=G$ for any conceivable groups $G$ as fundamental group.
We refine Epstein's method to prove joint concavity/convexity of matrix trace functions of Lieb type $\mathrm{Tr}\,f(Φ(A^p)^{1/2}Ψ(B^q)Φ(A^p)^{1/2})$ and symmetric (anti-) norm functions of the form $\|f(Φ(A^p)\,σ\,Ψ(B^q))\|$, where $Φ$ and $Ψ$ are positive linear maps, $σ$ is an operator mean, and $f(x^γ)$ with a certain power $γ$ is an operator monotone function on $(0,\infty)$. Moreover, the variational method of Carlen, Frank and Lieb is extended to general non-decreasing convex/concave functions on $(0,\infty)$ so that we prove joint concavity/convexity of more trace functions of Lieb typ…
We generalise the formula expressing the matrix trace of a given square matrix as the integral of the numerical values of $A$ over the Euclidean sphere to the unit spheres of finite-dimensional normed spaces that have a 1-symmetric basis. Our result is new even in the case of $\ell_p$-norms in $\mathbb{R}^N$ for $p\neq 2$.
We prove trace theorems for weighted mixed norm Sobolev spaces in the upper-half space where the weight is a power function of the vertical variable. The results show the differentiability order of the trace functions depends only on the power in the weight function and the integrability power for the integration with respect to the vertical variable but not on the integrability powers for the integration with respect to the horizontal ones. They are new even in the un-weighted case and they recover classical results in the case of un-mixed norm spaces. The work is motivated by the study of re…
In this note we present the metric approximation property for weighted mixed-norm $L_w^{(p_1,\dots ,p_n)}$ and variable exponent Lebesgue type spaces. As a consequence, this also implies the same property for modulation and Wiener-Amalgam spaces. We then characterise nuclear operators on such spaces and state the corresponding Grothendieck-Lidskii trace formulae. We apply the obtained results to derive criteria for nuclearity and trace formulae for periodic operators on $\mathbb R^n$ and functions of the harmonic oscillator in terms of the global symbol.
We refine Epstein's method to prove joint concavity/convexity of matrix trace functions of the extended Lieb type $Tr{Φ(A^p)^{1/2}Ψ(B^q)Φ(A^p)^{1/2}}^s$, where $Φ$ and $Ψ$ are positive linear maps. By the same method combined with majorization technique, similar properties are proved for symmetric (anti-) norm functions of the form $||{Φ(A^p)σΨ(B^q)}^s||$ involving an operator mean $σ$. Carlen and Lieb's variational method is also used to improve the convexity property of norm functions $||Φ(A^p)^s||$.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。