Naohito Tomita
It is known that the Sobolev space $L^2_s$ with $s>n/2$ appeared in the Hörmander multiplier theorem can be replaced by the Besov space $B^{2,1}_{n/2}$. On the other hand, the Besov space $B_{n/2}^{2,1}$ is continuously embedded in the modulation space $M^{2,1}_0$. In this paper, we consider the problem whether we can replace $B_{n/2}^{2,1}$ by $M^{2,1}_0$.
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
The aim of the article is to show a H{ö}rmander spectral multiplier theorem for an operator $A$ whose kernel of the semigroup $\exp(-zA)$ satisfies certain Poisson estimates for complex times $z.$ Here $\exp(-zA)$ acts on $L^p(Ω),\,1 < p < \infty,$ where $Ω$ is a space of homogeneous type with the additional condition that the measure of annuli is controlled. In most of the known H{ö}rmander type theorems in the literature, Gaussian bounds and self-adjointness for the semigroup are needed, whereas here the new feature is that the assumptions are the to some extend weaker Poisson bounds, and $\…
Let $A$ be a generator of an analytic semigroup having a H{ö}rmander functional calculus on $X = L^p(Ω,Y)$, where $Y$ is a UMD lattice. Using methods from Banach space geometry in connection with functional calculus, we show that for H{ö}rmander spectral multipliers decaying sufficiently fast at $\infty$, there holds a maximal estimate $\| \sup_{t \geq 0} |m(tA)f|\, \|_{L^p(Ω,Y)} \lesssim \|f\|_{L^p(Ω,Y)}$. We also show square function estimates $\left\| \left( \sum_k \sup _{t \geq 0} |m_k(tA)f_k|^2 \right)^{\frac12} \right\|_{L^p(Ω,Y)} \lesssim \left\| \left( \sum _k |f_k|^2 \right)^{\frac12}…
Let $A$ be a $0$-sectorial operator with a bounded $H^\infty(Σ\_σ)$-calculus for some $σ\in (0,π),$ e.g. a Laplace type operator on $L^p(Ω),\: 1 < p < \infty,$ where $Ω$ is a manifold or a graph. We show that $A$ has a H{ö}rmander functional calculus if and only if certain operator families derived from the resolvent $(λ- A)^{-1},$ the semigroup $e^{-zA},$ the wave operators $e^{itA}$ or the imaginary powers $A^{it}$ of $A$ are $R$-bounded in an $L^2$-averaged sense. If $X$ is an $L^p(Ω)$ space with $1 \leq p < \infty,$ $R$-boundedness reduces to well-known estimates of square sums.
In this paper we extend classical Titchmarsh theorems on the Fourier transform of H$\ddot{\text{o}}$lder-Lipschitz functions to the setting of harmonic $NA$ groups, which relate smoothness properties of functions to the growth and integrability of their Fourier transform. We prove a Fourier multiplier theorem for $L^2$-H$\ddot{\text{o}}$lder-Lipschitz spaces on Harmonic $NA$ groups. We also derive conditions and a characterisation of Dini-Lipschitz classes on Harmonic $NA$ groups in terms of the behaviour of their Fourier transform. Then, we shift our attention to the spherical analysis on Har…
Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents
本文将Fourier乘子、伪微分算子及Fourier积分算子的连续性与波前性质推广到Orlicz空间，并揭示Young函数与相应Lebesgue指数之间的联系。
We study the continuity on the modulation spaces $M^{p,q}$ of Fourier multipliers with symbols of the type $e^{iμ(ξ)}$, for some real-valued function $μ(ξ)$. A number of results are known, assuming that the derivatives of order $\geq 2$ of the phase $μ(ξ)$ are bounded or, more generally, that its second derivatives belong to the Sjöstrand class $M^{\infty,1}$. Here we extend those results, by assuming that the second derivatives lie in the bigger Wiener amalgam space $W(\mathcal{F} L^1,L^\infty)$; in particular they could have stronger oscillations at infinity such as $\cos |ξ|^2$. Actually ou…
We prove the boundedness of a general class of multipliers and Fourier multipliers, in particular of the Hilbert transform, on quasi-Banach modulation spaces. We also deduce boundedness for multiplications and convolutions for elements in such spaces.
We investigate the boundedness of unimodular Fourier multipliers on modulation spaces. Surprisingly, the multipliers with general symbol $e^{i|ξ|^α}$, where $α\in[0, 2]$, are bounded on all modulation spaces, but, in general, fail to be bounded on the usual $L^p$-spaces. As a consequence, the phase-space concentration of the solutions to the free Schrödinger and wave equations are preserved. As a byproduct, we also obtain boundedness results on modulation spaces for singular multipliers $|ξ|^{-δ} \sin (|ξ|^α)$ for $ 0 \leq δ\leq α$.
We study some fundamental properties of the special affine Fourier transform (SAFT) in connection with the Fourier analysis and time-frequency analysis. We introduce the modulation space $\boldsymbol {M}^{r,s}_A$ in connection with SAFT and prove that if a bounded linear operator between new modulation spaces commutes with $A$-translation, then it is a $A$-convolution operator. We also establish Hörmander multiplier theorem and Littlewood-Paley theorem associated with the SAFT.
In this paper we have studied Fourier multipliers and Littlewood-Paley square functions in the context of modulation spaces. We have also proved that any bounded linear operator from modulation space $\mathcal{M}_{p,q}(\R^n), 1\leq p,q\leq \infty,$ into itself possesses an $l_2-$valued extension. This is an analogue of a well known result due to Marcinkiewicz and Zygmund on classical $L^p-$spaces.
We indicate how to construct a family of modulation function spaces that have a scaling symmetry. We also illustrate the behavior of the Schrödinger multiplier on such function spaces.
The inclusion relations between the $L^p$-Sobolev spaces and the modulation spaces is determined explicitly. As an application, mapping properties of unimodular Fourier multiplier $e^{i|D|^α}$ between $L^p$-Sobolev spaces and modulation spaces are discussed.
Subdyadic time-frequency analysis: Gabor frames, modulation spaces, and Miyachi multipliers
本文提出基于子二分几何的时间-频率分析框架，构建稳定Gabor框架和调制空间，并发展Miyachi乘法理论，为微局分析和高频数值方案提供统一工具。
Fourier Multipliers on Quasi-Banach Orlicz Spaces and Orlicz Modulation Spaces
本文证明Fourier乘子从L^Φ1到L^Φ2的连续性可推广至Orlicz调制空间，并应用于Mihlin和Hörmander定理，最后给出特定符号乘子在拟Banach Orlicz调制空间上的有界性条件。
Phase space analysis of spectral multipliers for the twisted Laplacian
本文利用元辛等价与转移原理，在调制空间和Wiener amalgam空间中研究扭曲拉普拉斯算子谱乘子的有界性，并完整刻画了其热流及分数阶热流的有界性。
$q$-variational H{ö}rmander functional calculus and Schr{ö}dinger and wave maximal estimates
本文在扇形算子满足Hörmander泛函演算的条件下，证明m(tA)f对几乎处处变量具有有限q-变差（q>2），推广了半群情形；并进一步建立依赖时间的极大估计，应用于Schrödinger与波动方程传播子，得到Carleson型逐点收敛结果。
The Lifting Property for Frame Multipliers and Toeplitz Operators
本文证明正符号框架乘子是coorbit空间间的Banach同构，推广提升定理至Gabor框架和Fock空间，得到调制空间与加权Fock空间的新同构结果。
We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be formulated in terms of projection operators on the Bargmann-Fock spaces of entire functions. Specifically for signals in $L^2(\mathbb{R}^d)$, we obtain norm estimates of Daubechies' time-frequency localization operator localizing on porous sets. The proof is based on the maximal Nyquist density of such sets, and for multidimensional Cantor iterates we derive explicit upper bound…
We study the range of time-frequency localization operators acting on modulation spaces and prove a lifting theorem. As an application we also characterize the range of Gabor multipliers, and, in the realm of complex analysis, we characterize the range of certain Toeplitz operators on weighted Bargmann-Fock spaces. The main tools are the construction of canonical isomorphisms between modulation spaces of Hilbert-type and a refined version of the spectral invariance of pseudodifferential operators. On the technical level we prove a new class of inequalities for weighted gamma functions.
We study a class of almost diagonal matrices compatible with the mixed-norm $α$-modulation spaces $M_{\vec{p},q}^{s,α}(\mathbb{R}^n)$, $α\in [0,1]$, introduced recently by Cleanthous and Georgiadis [Trans.\ Amer.\ Math.\ Soc.\ 373 (2020), no. 5, 3323-3356]. The class of almost diagonal matrices is shown to be closed under matrix multiplication and we connect the theory to the continuous case by identifying a suitable notion of molecules for the mixed-norm $α$-modulation spaces. We show that the "change of frame" matrix for a pair of time-frequency frames for the mixed-norm $α$-modulation consi…
We prove that the class of trilinear multiplier forms with singularity over a one dimensional subspace, including the bilinear Hilbert transform, admit bounded $L^p$-extension to triples of intermediate $\mathrm{UMD}$ spaces. No other assumption, for instance of Rademacher maximal function type, is made on the triple of $\mathrm{UMD}$ spaces. Among the novelties in our analysis is an extension of the phase-space projection technique to the $\mathrm{UMD}$-valued setting. This is then employed to obtain appropriate single tree estimates by appealing to the $\mathrm{UMD}$-valued bound for bilinea…
Comparisons between Fourier and STFT multipliers: the smoothing effect of the Short-time Fourier Transform
本文比较傅里叶乘子与STFT乘子，给出二者相等的充分必要条件，并揭示STFT乘子因双窗短时傅里叶变换而具有平滑效应，同时得到反Wick算子连续性的必要条件及离散Gabor乘子的对应结果。
Localization Operators On Discrete Modulation Spaces
本文在离散格点上定义短时 Fourier 变换与调制空间，系统研究时频局部化算子的有界性、紧性、Schatten–von Neumann 性质及其与 Landau–Pollak–Slepian 型算子的关系，并证明其在符号条件下可成为仿交换子、仿积和 Fourier 乘子。
The Concept of Wiener Amalgam Spaces
本文回顾 Wiener 融合空间的基本性质，展示其在调和分析中的广泛应用，包括改进 Hausdorff-Young 定理、证明 Sobolev 嵌入定理以及确定 Sobolev 代数的点态乘子。
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。