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On Ultradifferentiable Regularity of Perturbations by Lower Order Terms of Globally $$C^infty$$ Hypoelliptic Ultradifferentiable Pseudodifferential Operators 论全球$$C^infty$$次椭圆超微分伪微分算子低阶项扰动的超微分正则性
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-12-29 DOI: 10.1007/s00041-023-10057-9
Igor Ambo Ferra, Gerson Petronilho
{"title":"On Ultradifferentiable Regularity of Perturbations by Lower Order Terms of Globally $$C^infty$$ Hypoelliptic Ultradifferentiable Pseudodifferential Operators","authors":"Igor Ambo Ferra, Gerson Petronilho","doi":"10.1007/s00041-023-10057-9","DOIUrl":"https://doi.org/10.1007/s00041-023-10057-9","url":null,"abstract":"<p>We prove <span>({mathcal {M}})</span>-regularity for a class of pseudodifferential operators in ultradifferentiable classes defined on the torus <span>(mathbb {T}^{m+n})</span> which are globally <span>(C^{infty })</span> hypoelliptic. The same property is also valid for certain perturbations of these operators by lower order terms.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139063589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Trigonometric Polynomials with Frequencies in the Set of Squares and Divisors in a Short Interval 在短间隔内具有平方和除数集合中频率的三角多项式
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-12-19 DOI: 10.1007/s00041-023-10064-w
{"title":"Trigonometric Polynomials with Frequencies in the Set of Squares and Divisors in a Short Interval","authors":"","doi":"10.1007/s00041-023-10064-w","DOIUrl":"https://doi.org/10.1007/s00041-023-10064-w","url":null,"abstract":"<h3>Abstract</h3> <p>Let <span> <span>(gamma _0=frac{sqrt{5}-1}{2}=0.618ldots )</span> </span>. We prove that, for any <span> <span>(varepsilon &gt;0)</span> </span> and any trigonometric polynomial <em>f</em> with frequencies in the set <span> <span>({n^2: N leqslant nleqslant N+N^{gamma _0-varepsilon }})</span> </span>, the inequality <span> <span>$$begin{aligned} Vert fVert _4 ll varepsilon ^{-1/4}Vert fVert _2 end{aligned}$$</span> </span>holds, which makes a progress on a conjecture of Cilleruelo and Córdoba. We also present a connection between this conjecture and the conjecture of Ruzsa which asserts that, for any <span> <span>(varepsilon &gt;0)</span> </span>, there is <span> <span>(C(varepsilon )&gt;0)</span> </span> such that each positive integer <em>N</em> has at most <span> <span>(C(varepsilon ))</span> </span> divisors in the interval <span> <span>([N^{1/2}, N^{1/2}+N^{1/2-varepsilon }])</span> </span>.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138818628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp Hardy’s Inequality for Orthogonal Expansions in  $$H^p$$  Spaces $$H^p$$ 空间中正交展开的夏普-哈代不等式
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-12-19 DOI: 10.1007/s00041-023-10060-0
Paweł Plewa
{"title":"Sharp Hardy’s Inequality for Orthogonal Expansions in  $$H^p$$  Spaces","authors":"Paweł Plewa","doi":"10.1007/s00041-023-10060-0","DOIUrl":"https://doi.org/10.1007/s00041-023-10060-0","url":null,"abstract":"<p>Hardy’s inequality on <span>(H^p)</span> spaces, <span>(pin (0,1])</span>, in the context of orthogonal expansions is investigated for general bases on a wide class of domains in <span>(mathbb {R}^d)</span> with Lebesgue measure. The obtained result is applied to various Hermite, Laguerre, and Jacobi expansions. For that purpose some delicate estimates of the higher order derivatives for the underlying functions and of the associated heat or Poison kernels are proved. Moreover, sharpness of studied Hardy’s inequalities is justified by a construction of an explicit counterexample, which is adjusted to all considered settings.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138821804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform Resolvent Estimates for Laplace–Beltrami Operator on the Flat Euclidean Cone 平面欧几里得锥上Laplace-Beltrami算子的一致分辨估计
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-12-01 DOI: 10.1007/s00041-023-10056-w
Jialu Wang, Chengbin Xu
{"title":"Uniform Resolvent Estimates for Laplace–Beltrami Operator on the Flat Euclidean Cone","authors":"Jialu Wang, Chengbin Xu","doi":"10.1007/s00041-023-10056-w","DOIUrl":"https://doi.org/10.1007/s00041-023-10056-w","url":null,"abstract":"<p>We study the <span>(L^prightarrow L^q)</span>-type uniform resolvent estimate for Laplace –Beltrami operator on the flat Euclidean cone <span>(C(mathbb {S}_{sigma }^1)triangleq mathbb {R}_{+}times (mathbb {R}/2pi sigma mathbb {Z}))</span> equipped with the metric <span>(g(r,theta )=dr^2+r^2dtheta ^2)</span> where the circle of radius <span>(sigma &gt;0)</span>. The key ingredient is the resolvent kernel constructed by Zhang in (J Funct Anal 282(3):109311, 2022) and the Young inequality holds under the monotonicity assumption on the flat Euclidean cone.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Components and Exit Times of Brownian Motion in Two or More p-Adic Dimensions 两个或多个p进维布朗运动的分量和退出时间
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-11-20 DOI: 10.1007/s00041-023-10053-z
Rahul Rajkumar, David Weisbart
{"title":"Components and Exit Times of Brownian Motion in Two or More p-Adic Dimensions","authors":"Rahul Rajkumar, David Weisbart","doi":"10.1007/s00041-023-10053-z","DOIUrl":"https://doi.org/10.1007/s00041-023-10053-z","url":null,"abstract":"<p>The fundamental solution to a pseudo-differential equation for functions defined on the <i>d</i>-fold product of the <i>p</i>-adic numbers, <span>(mathbb {Q}_p)</span>, induces an analogue of the Wiener process in <span>(mathbb {Q}_p^d)</span>. As in the real setting, the components are 1-dimensional <i>p</i>-adic Brownian motions with the same diffusion constant and exponent as the original process. Asymptotic analysis of the conditional probabilities shows that the vector components are dependent for all time. Exit time probabilities for the higher dimensional processes reveal a concrete effect of the component dependency.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
$$L^p$$ - $$L^q$$ Boundedness of Fourier Multipliers Associated with the Anharmonic Oscillator $$L^p$$ - $$L^q$$与非谐振子相关的傅里叶乘法器的有界性
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-11-20 DOI: 10.1007/s00041-023-10047-x
Marianna Chatzakou, Vishvesh Kumar
{"title":"$$L^p$$ - $$L^q$$ Boundedness of Fourier Multipliers Associated with the Anharmonic Oscillator","authors":"Marianna Chatzakou, Vishvesh Kumar","doi":"10.1007/s00041-023-10047-x","DOIUrl":"https://doi.org/10.1007/s00041-023-10047-x","url":null,"abstract":"<p>In this paper we study the <span>(L^p)</span>-<span>(L^q)</span> boundedness of the Fourier multipliers in the setting where the underlying Fourier analysis is introduced with respect to the eigenfunctions of an anharmonic oscillator <i>A</i>. Using the notion of a global symbol that arises from this analysis, we extend a version of the Hausdorff–Young–Paley inequality that guarantees the <span>(L^p)</span>-<span>(L^q)</span> boundedness of these operators for the range <span>(1&lt;p le 2 le q &lt;infty )</span>. The boundedness results for spectral multipliers acquired, yield as particular cases Sobolev embedding theorems and time asymptotics for the <span>(L^p)</span>-<span>(L^q)</span> norms of the heat kernel associated with the anharmonic oscillator. Additionally, we consider functions <i>f</i>(<i>A</i>) of the anharmonic oscillator on modulation spaces and prove that Linskĭi’s trace formula holds true even when <i>f</i>(<i>A</i>) is simply a nuclear operator.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
A Note on the Operator Window of Modulation Spaces 调制空间算子窗的一个注记
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-11-20 DOI: 10.1007/s00041-023-10055-x
Weichao Guo, Guoping Zhao
{"title":"A Note on the Operator Window of Modulation Spaces","authors":"Weichao Guo, Guoping Zhao","doi":"10.1007/s00041-023-10055-x","DOIUrl":"https://doi.org/10.1007/s00041-023-10055-x","url":null,"abstract":"<p>Inspired by the recent article Skrettingland (J. Fourier Anal. Appl. <b>28</b>(2), 1–34 (2022)), this paper is devoted to the study of a suitable class of windows in the framework of bounded linear operators on <span>(L^2({{mathbb {R}}}^{d}))</span>. We establish a natural and complete characterization for the window class such that the corresponding STFT leads to equivalent norms on modulation spaces. The positive bounded linear operators are also characterized by its Cohen’s class distributions such that the corresponding quantities form equivalent norms on modulation spaces. As a generalization, we introduce a family of operator classes corresponding to the operator-valued modulation spaces. Some applications of our main theorems to the localization operators are also concerned.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Refinements of Berry–Esseen Inequalities in Terms of Lyapunov Coefficients 关于Lyapunov系数的Berry-Esseen不等式的改进
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-11-16 DOI: 10.1007/s00041-023-10054-y
Sergey G. Bobkov
{"title":"Refinements of Berry–Esseen Inequalities in Terms of Lyapunov Coefficients","authors":"Sergey G. Bobkov","doi":"10.1007/s00041-023-10054-y","DOIUrl":"https://doi.org/10.1007/s00041-023-10054-y","url":null,"abstract":"<p>We discuss some variants of the Berry–Esseen inequality in terms of Lyapunov coefficients which may provide sharp rates of normal approximation.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Young’s Inequality for the Twisted Convolution 扭曲卷积的杨氏不等式
3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-11-01 DOI: 10.1007/s00041-023-10051-1
P. K. Ratnakumar
{"title":"Young’s Inequality for the Twisted Convolution","authors":"P. K. Ratnakumar","doi":"10.1007/s00041-023-10051-1","DOIUrl":"https://doi.org/10.1007/s00041-023-10051-1","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135270975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uncertainty Principle for Free Metaplectic Transformation 自由元塑性变换的不确定性原理
3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2023-11-01 DOI: 10.1007/s00041-023-10052-0
Zhichao Zhang
{"title":"Uncertainty Principle for Free Metaplectic Transformation","authors":"Zhichao Zhang","doi":"10.1007/s00041-023-10052-0","DOIUrl":"https://doi.org/10.1007/s00041-023-10052-0","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135325999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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