发布求助
文献互助 智能选刊 最新文献

Journal of Fourier Analysis and Applications最新文献

筛选
英文 中文
On the Boundedness of Non-standard Rough Singular Integral Operators 论非标准粗糙奇异积分算子的有界性
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-05-10 DOI: 10.1007/s00041-024-10086-y
Guoen Hu, Xiangxing Tao, Zhidan Wang, Qingying Xue
{"title":"On the Boundedness of Non-standard Rough Singular Integral Operators","authors":"Guoen Hu, Xiangxing Tao, Zhidan Wang, Qingying Xue","doi":"10.1007/s00041-024-10086-y","DOIUrl":"https://doi.org/10.1007/s00041-024-10086-y","url":null,"abstract":"<p>Let <span>(Omega )</span> be a homogeneous function of degree zero, have vanishing moment of order one on the unit sphere <span>(mathbb {S}^{d-1})</span>(<span>(dge 2)</span>). In this paper, our object of investigation is the following rough non-standard singular integral operator </p><span>$$begin{aligned} T_{Omega ,,A}f(x)=mathrm{p.,v.}int _{{mathbb {R}}^d}frac{Omega (x-y)}{|x-y|^{d+1}}big (A(x)-A(y)-nabla A(y)(x-y)big )f(y)textrm{d}y, end{aligned}$$</span><p>where <i>A</i> is a function defined on <span>({mathbb {R}}^d)</span> with derivatives of order one in <span>({textrm{BMO}}({mathbb {R}}^d))</span>. We show that <span>(T_{Omega ,,A})</span> enjoys the endpoint <span>(Llog L)</span> type estimate and is <span>(L^p)</span> bounded if <span>(Omega in L(log L)^{2}({mathbb {S}}^{d-1}))</span>. These results essentially improve the previous known results given by Hofmann (Stud Math 109:105–131, 1994) for the <span>(L^p)</span> boundedness of <span>(T_{Omega ,,A})</span> under the condition <span>(Omega in L^{q}({mathbb {S}}^{d-1}))</span> <span>((q&gt;1))</span>, Hu and Yang (Bull Lond Math Soc 35:759–769, 2003) for the endpoint weak <span>(Llog L)</span> type estimates when <span>(Omega in textrm{Lip}_{alpha }({mathbb {S}}^{d-1}))</span> for some <span>(alpha in (0,,1])</span>.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"65 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939910","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
Existence of Exponential Orthonormal Bases for Infinite Convolutions on $${{mathbb {R}}}^n$$ $${{mathbb {R}}^n$ 上无限卷积的指数正则基的存在性
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-05-07 DOI: 10.1007/s00041-024-10088-w
Yan-Song Fu, Min-Wei Tang
{"title":"Existence of Exponential Orthonormal Bases for Infinite Convolutions on $${{mathbb {R}}}^n$$","authors":"Yan-Song Fu, Min-Wei Tang","doi":"10.1007/s00041-024-10088-w","DOIUrl":"https://doi.org/10.1007/s00041-024-10088-w","url":null,"abstract":"<p>In this paper we investigate the harmonic analysis of infinite convolutions generated by admissible pairs on Euclidean space <span>({{mathbb {R}}}^n)</span>. Our main results give several sufficient conditions so that the infinite convolution <span>(mu )</span> to be a spectral measure, that is, its Hilbert space <span>(L^2(mu ))</span> admits a family of orthonormal basis of exponentials. As a concrete application, we give a complete characterization on the spectral property for certain infinite convolution on the plane <span>({{mathbb {R}}}^2)</span> in terms of admissible pairs.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"65 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940018","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
On the Sharp Estimates for Convolution Operators with Oscillatory Kernel 论具有振荡核的卷积算子的夏普估计值
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-05-02 DOI: 10.1007/s00041-024-10085-z
Isroil A. Ikromov, Dildora I. Ikromova
{"title":"On the Sharp Estimates for Convolution Operators with Oscillatory Kernel","authors":"Isroil A. Ikromov, Dildora I. Ikromova","doi":"10.1007/s00041-024-10085-z","DOIUrl":"https://doi.org/10.1007/s00041-024-10085-z","url":null,"abstract":"<p>In this article, we studied the convolution operators <span>(M_k)</span> with oscillatory kernel, which are related to the solutions of the Cauchy problem for the strictly hyperbolic equations. The operator <span>(M_k)</span> is associated to the characteristic hypersurfaces<span>(Sigma subset {mathbb {R}}^3)</span> of a hyperbolic equation and smooth amplitude function, which is homogeneous of the order <span>(-k)</span> for large values of the argument. We investigated the convolution operators assuming that the corresponding amplitude function is contained in a sufficiently small conic neighborhood of a given point <span>(vin Sigma )</span> at which, exactly one of the principal curvatures of the surface <span>(Sigma )</span> does not vanish. Such surfaces exhibit singularities of the type <i>A</i> in the sense of Arnold’s classification. Denoting by <span>(k_p)</span> the minimal number such that <span>(M_k)</span> is <span>(L^pmapsto L^{p'})</span>-bounded for <span>(k&gt;k_p,)</span> we showed that the number <span>(k_p)</span> depends on some discrete characteristics of the surface <span>(Sigma )</span>.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887480","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
Extrapolation of Compactness on Banach Function Spaces 巴拿赫函数空间的紧凑性外推法
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-05-02 DOI: 10.1007/s00041-024-10087-x
Emiel Lorist, Zoe Nieraeth
{"title":"Extrapolation of Compactness on Banach Function Spaces","authors":"Emiel Lorist, Zoe Nieraeth","doi":"10.1007/s00041-024-10087-x","DOIUrl":"https://doi.org/10.1007/s00041-024-10087-x","url":null,"abstract":"<p>We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator <i>T</i> in the weighted Lebesgue scale and the compactness of <i>T</i> in the unweighted Lebesgue scale yields compactness of <i>T</i> on a very general class of Banach function spaces. As our main new tool, we prove various characterizations of the boundedness of the Hardy-Littlewood maximal operator on such spaces and their associate spaces, using a novel sparse self-improvement technique. We apply our main results to prove compactness of the commutators of singular integral operators and pointwise multiplication by functions of vanishing mean oscillation on, for example, weighted variable Lebesgue spaces.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"42 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887467","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
Compact Embeddings for Fractional Super and Sub Harmonic Functions with Radial Symmetry 具有径向对称性的分数超和次谐函数的紧凑嵌入
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-04-18 DOI: 10.1007/s00041-024-10082-2
Jacopo Bellazzini, Vladimir Georgiev
{"title":"Compact Embeddings for Fractional Super and Sub Harmonic Functions with Radial Symmetry","authors":"Jacopo Bellazzini, Vladimir Georgiev","doi":"10.1007/s00041-024-10082-2","DOIUrl":"https://doi.org/10.1007/s00041-024-10082-2","url":null,"abstract":"<p>We prove compactness of the embeddings in Sobolev spaces for fractional super and sub harmonic functions with radial symmetry. The main tool is a pointwise decay for radially symmetric functions belonging to a function space defined by finite homogeneous Sobolev norm together with finite <span>(L^2)</span> norm of the Riesz potentials. As a byproduct we prove also existence of maximizers for the interpolation inequalities in Sobolev spaces for radially symmetric fractional super and sub harmonic functions.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630054","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
Multi-parameter Maximal Fourier Restriction 多参数最大傅立叶限制
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-04-17 DOI: 10.1007/s00041-024-10083-1
Aleksandar Bulj, Vjekoslav Kovač
{"title":"Multi-parameter Maximal Fourier Restriction","authors":"Aleksandar Bulj, Vjekoslav Kovač","doi":"10.1007/s00041-024-10083-1","DOIUrl":"https://doi.org/10.1007/s00041-024-10083-1","url":null,"abstract":"<p>The main result of this note is the strengthening of a quite arbitrary a priori Fourier restriction estimate to a multi-parameter maximal estimate of the same type. This allows us to discuss a certain multi-parameter Lebesgue point property of Fourier transforms, which replaces Euclidean balls by standard ellipsoids or axes-parallel rectangles. Along the lines of the same proof, we also establish a <i>d</i>-parameter Menshov–Paley–Zygmund-type theorem for the Fourier transform on <span>({mathbb {R}}^d)</span>. Such a result is interesting for <span>(dgeqslant 2)</span> because, in a sharp contrast with the one-dimensional case, the corresponding endpoint <span>({text {L}}^2)</span> estimate (i.e., a Carleson-type theorem) is known to fail since the work of C. Fefferman in 1970. Finally, we show that a Strichartz estimate for a given homogeneous constant-coefficient linear dispersive PDE can sometimes be strengthened to a certain pseudo-differential version.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608891","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 Boundedness of Sequence of Operators Associated with the Walsh System and Their Pointwise Convergence 与沃尔什系统相关的算子序列的均匀有界性及其点式收敛性
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-04-15 DOI: 10.1007/s00041-024-10081-3
Ushangi Goginava, Farrukh Mukhamedov
{"title":"Uniform Boundedness of Sequence of Operators Associated with the Walsh System and Their Pointwise Convergence","authors":"Ushangi Goginava, Farrukh Mukhamedov","doi":"10.1007/s00041-024-10081-3","DOIUrl":"https://doi.org/10.1007/s00041-024-10081-3","url":null,"abstract":"<p>Revisiting the main point of the almost everywhere convergence, it becomes clear that a weak (1,1)-type inequality must be established for the maximal operator corresponding to the sequence of operators. The better route to take in obtaining almost everywhere convergence is by using the uniform boundedness of the sequence of operator, instead of using the mentioned maximal type of inequality. In this paper it is proved that a sequence of operators, defined by matrix transforms of the Walsh–Fourier series, is convergent almost everywhere to the function <span>(fin L_{1})</span> if they are uniformly bounded from the dyadic Hardy space <span>(H_{1} left( {mathbb {I}}right) )</span> to <span>(L_{1}left( mathbb {I}right) )</span>. As a further matter, the characterization of the points are put forth where the sequence of the operators of the matrix transform is convergent.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"3 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571292","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 Global Well-Posedness for the Cubic Nonlinear Schrödinger Equation with Third Order Dispersion 具有三阶分散性的立方非线性薛定谔方程的尖锐全局解析性
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-04-15 DOI: 10.1007/s00041-024-10084-0
X. Carvajal, M. Panthee
{"title":"Sharp Global Well-Posedness for the Cubic Nonlinear Schrödinger Equation with Third Order Dispersion","authors":"X. Carvajal, M. Panthee","doi":"10.1007/s00041-024-10084-0","DOIUrl":"https://doi.org/10.1007/s00041-024-10084-0","url":null,"abstract":"<p>We consider the initial value problem (IVP) associated to the cubic nonlinear Schrödinger equation with third-order dispersion </p><span>$$begin{aligned} partial _{t}u+ialpha partial ^{2}_{x}u- partial ^{3}_{x}u+ibeta |u|^{2}u = 0, quad x,t in mathbb R, end{aligned}$$</span><p>for given data in the Sobolev space <span>(H^s(mathbb R))</span>. This IVP is known to be locally well-posed for given data with Sobolev regularity <span>(s&gt;-frac{1}{4})</span> and globally well-posed for <span>(sge 0)</span> (Carvajal in Electron J Differ Equ 2004:1–10, 2004). For given data in <span>(H^s(mathbb R))</span>, <span>(0&gt;s&gt; -frac{1}{4})</span> no global well-posedness result is known. In this work, we derive an <i>almost conserved quantity</i> for such data and obtain a sharp global well-posedness result. Our result answers the question left open in (Carvajal in Electron J Differ Equ 2004:1–10, 2004).</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"234 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fourier Transform for $$L^p$$ -Functions with a Vector Measure on a Homogeneous Space of Compact Groups 紧凑群同质空间上具有向量量度的 $$L^p$$ 函数的傅里叶变换
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-04-11 DOI: 10.1007/s00041-024-10077-z
Sorravit Phonrakkhet, Keng Wiboonton
{"title":"Fourier Transform for $$L^p$$ -Functions with a Vector Measure on a Homogeneous Space of Compact Groups","authors":"Sorravit Phonrakkhet, Keng Wiboonton","doi":"10.1007/s00041-024-10077-z","DOIUrl":"https://doi.org/10.1007/s00041-024-10077-z","url":null,"abstract":"<p>Let <i>G</i> be a compact group and <i>G</i>/<i>H</i> a homogeneous space where <i>H</i> is a closed subgroup of <i>G</i>. Define an operator <span>(T_H:C(G) rightarrow C(G/H))</span> by <span>(T_Hf(tH)=int _H f(th) , dh)</span> for each <span>(tH in G/H)</span>. In this paper, we extend <span>(T_H)</span> to a norm-decreasing operator between <span>(L^p)</span>-spaces with a vector measure for each <span>(1 le p &lt;infty )</span>. This extension will be used to derive properties of invariant vector measures on <i>G</i>/<i>H</i>. Moreover, a definition of the Fourier transform for <span>(L^p)</span>-functions with a vector measure is introduced on <i>G</i>/<i>H</i>. We also prove the uniqueness theorem and the Riemann–Lebesgue lemma.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"48 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An $$L^p$$ -Spectral Multiplier Theorem with Sharp p-Specific Regularity Bound on Heisenberg Type Groups 海森堡类型群上具有 p 特定锐正则约束的 $$L^p$$ 谱乘数定理
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-04-04 DOI: 10.1007/s00041-024-10075-1
{"title":"An $$L^p$$ -Spectral Multiplier Theorem with Sharp p-Specific Regularity Bound on Heisenberg Type Groups","authors":"","doi":"10.1007/s00041-024-10075-1","DOIUrl":"https://doi.org/10.1007/s00041-024-10075-1","url":null,"abstract":"<h3>Abstract</h3> <p>We prove an <span> <span>(L^p)</span> </span>-spectral multiplier theorem for sub-Laplacians on Heisenberg type groups under the sharp regularity condition <span> <span>(s&gt;dleft| 1/p-1/2right| )</span> </span>, where <em>d</em> is the topological dimension of the underlying group. Our approach relies on restriction type estimates where the multiplier is additionally truncated along the spectrum of the Laplacian on the center of the group.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"59 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571286","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信