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Journal of Pseudo-Differential Operators and Applications最新文献

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Sharp reverse fractional Hausdorff inequality on power-weighted Lebesgue spaces 幂加权勒贝格空间上的锐反向分数豪斯多夫不等式
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-07-16 DOI: 10.1007/s11868-024-00629-8
Xiaoyu Liu, Mingquan Wei, Pengchao Song, Dunyan Yan
{"title":"Sharp reverse fractional Hausdorff inequality on power-weighted Lebesgue spaces","authors":"Xiaoyu Liu, Mingquan Wei, Pengchao Song, Dunyan Yan","doi":"10.1007/s11868-024-00629-8","DOIUrl":"https://doi.org/10.1007/s11868-024-00629-8","url":null,"abstract":"<p>Our main focus in this paper is to explore the mapping properties for the <i>n</i>-dimensional fractional Hausdorff operator <span>(H_{Phi ,beta })</span> from <span>(L^{p}(mathbb {R}^{n},|x|^{alpha }))</span> to <span>(L^{q}(mathbb {R}^{n},|x|^{gamma }))</span>, where <span>(p,q&lt;1~(p,qne 0))</span>, <span>(alpha ,gamma in mathbb {R})</span>, <span>(0le beta &lt;n)</span> and <span>(Phi )</span> is a nonnegative measurable function on <span>(mathbb {R}^n)</span>. For <span>(p,q&lt;1~(p,qne 0))</span> satisfying some additional assumptions, we give sufficient conditions for the validity of the reverse fractional Hausdorff inequality <span>(left| H_{Phi ,beta }fright| _{L^{q}(mathbb {R}^{n},|x|^{gamma })}ge CVert fVert _{L^{p}(mathbb {R}^{n},|x|^{alpha })})</span> for some positive constant <i>C</i> and all nonnegative functions <span>(fin L^{p}(mathbb {R}^{n},|x|^{alpha }))</span>. For the particular case <span>(0&lt;p=q&lt;1)</span>, we obtain the sharp reverse fractional Hausdorff inequality. As applications, we establish the sharp reverse inequalities for the <i>n</i>-dimensional fractional Hardy operator and its adjoint operator, and also the <i>n</i>-dimensional fractional Hardy–Littlewood–Pólya operator on power-weighted Lebesgue spaces.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"2013 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719748","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
Clifford-valued linear canonical wave-packet transform and corresponding uncertainty principles 克利福德值线性典型波包变换和相应的不确定性原理
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-07-09 DOI: 10.1007/s11868-024-00627-w
Shahbaz Rafiq, M. Younus Bhat
{"title":"Clifford-valued linear canonical wave-packet transform and corresponding uncertainty principles","authors":"Shahbaz Rafiq, M. Younus Bhat","doi":"10.1007/s11868-024-00627-w","DOIUrl":"https://doi.org/10.1007/s11868-024-00627-w","url":null,"abstract":"<p>In an effort to express Clifford-valued signals efficiently in time–frequency domain, we introduce the notion of the novel integral transform known as Clifford-valued linear canonical wave-packet transform (CLCWPT). In the beginning, we derived the fundamental properties of the proposed transform which include linearity, anti-linearity, scaling parity, dilation and Parseval’s formula. Moreover, some important signal analysis results have been established, viz. energy conservation, inversion formula, characterization of range and bounds of clifford valued linear canonical wave-packet transform. We culminate our manuscript by studying corresponding Heisenberg’s uncertainty principle and logarithmic uncertainty principle associated with CLCWPT.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"7 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567826","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 a class of Kirchhoff problems with nonlocal terms and logarithmic nonlinearity 关于一类具有非局部项和对数非线性的基尔霍夫问题
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-07-07 DOI: 10.1007/s11868-024-00624-z
El-Houari Hamza, Arhrrabi Elhoussain, J. Vanterler da da C. Sousa
{"title":"On a class of Kirchhoff problems with nonlocal terms and logarithmic nonlinearity","authors":"El-Houari Hamza, Arhrrabi Elhoussain, J. Vanterler da da C. Sousa","doi":"10.1007/s11868-024-00624-z","DOIUrl":"https://doi.org/10.1007/s11868-024-00624-z","url":null,"abstract":"<p>In this present paper, we concern investigating nonlinear Kirchhoff-type problems subject to Dirichlet boundary conditions, incorporating nonlocal terms and logarithmic nonlinearity in the <span>(phi )</span>-Hilfer fractional spaces with the <span>(eta (cdot ))</span>-Laplacian operator by means of the do Mountain Pass Theorem, Fountain Theorem and Dual Fountain Theorem.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"16 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567827","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
Pseudo-differential operators in several p-adic variables and sub-Markovian semigroups 若干 p-adic 变量中的伪微分算子和子马尔可夫半群
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-07-05 DOI: 10.1007/s11868-024-00623-0
Anselmo Torresblanca-Badillo, Edilberto Arroyo-Ortiz, Ronald Barrios-Garizao
{"title":"Pseudo-differential operators in several p-adic variables and sub-Markovian semigroups","authors":"Anselmo Torresblanca-Badillo, Edilberto Arroyo-Ortiz, Ronald Barrios-Garizao","doi":"10.1007/s11868-024-00623-0","DOIUrl":"https://doi.org/10.1007/s11868-024-00623-0","url":null,"abstract":"<p>This article marks the inaugural exploration of certain classes of negative or positive definite functions in several <i>p</i>-adic variables. Associated with these functions, two classes of pseudo-differential operators, convolution semigroups, some positive measures and <span>(L^{2}(mathbb {Q}_{p}^{n}))</span>-sub-Markovian semigroups are introduced.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"16 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567829","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
Continuity properties of multi-parameter pseudodifferential operators on Bony class 骨类上多参数伪微分算子的连续特性
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-07-05 DOI: 10.1007/s11868-024-00622-1
Wei Ding, Min Gu, Yueping Zhu
{"title":"Continuity properties of multi-parameter pseudodifferential operators on Bony class","authors":"Wei Ding, Min Gu, Yueping Zhu","doi":"10.1007/s11868-024-00622-1","DOIUrl":"https://doi.org/10.1007/s11868-024-00622-1","url":null,"abstract":"<p>It is well-known that the pseudodifferential operator with the symbol in Bony class, a subset of <span>(S_{1,1}^0(mathbb R^n))</span>, is bounded on <span>(L^{2}(mathbb {R}^{n}))</span>. The main purpose of this paper is to extend the classical results to multi-parameter case, i.e., to discuss the boundedness on <span>(L^2(mathbb {R}^{n_1+n_2}))</span> and on <span>(h^{p}(mathbb {R}^{n_{1}}times mathbb {R}^{n_{2}}) (0&lt;ple 1))</span> of multi-parameter pseudodifferential operator with symbol satisfying multi-parameter Bony conditions.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"16 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567828","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
Fractional type Marcinkiewicz integral and its commutator on grand variable Herz-Morrey spaces 大变量赫兹-莫雷空间上的分数型马尔钦凯维奇积分及其换元器
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-06-27 DOI: 10.1007/s11868-024-00621-2
Xijuan Chen, Guanghui Lu, Wenwen Tao
{"title":"Fractional type Marcinkiewicz integral and its commutator on grand variable Herz-Morrey spaces","authors":"Xijuan Chen, Guanghui Lu, Wenwen Tao","doi":"10.1007/s11868-024-00621-2","DOIUrl":"https://doi.org/10.1007/s11868-024-00621-2","url":null,"abstract":"<p>The aim of this paper is to establish the boundedness of the fractional type Marcinkiewicz integral operator <span>(mathcal {M}_{alpha ,rho ,m})</span> and its higher order commutator <span>(mathcal {M}_{alpha ,rho ,m,b^l})</span> generated by <span>(bin textrm{BMO}({mathbb {R}}^n))</span> and <span>(mathcal {M}_{alpha ,rho ,m})</span> on the weighted Lebesgue spaces <span>(L_omega ^p({mathbb {R}}^n))</span>. Under assumption that the variable exponents <span>(alpha (cdot ))</span> and <span>(q(cdot ))</span> satisfy the <span>(log )</span> decay at infinity and origin, the authors show that the <span>(mathcal {M}_{alpha ,rho ,m})</span> and <span>(mathcal {M}_{alpha ,rho ,m,b^l})</span> are bounded on the grand variable Herz spaces <span>(dot{K}_{q(cdot )}^{alpha (cdot ),p),theta }({mathbb {R}}^n))</span> and the grand variable Herz-Morrey spaces <span>(Mdot{K}_{p),theta ,q(cdot )}^{alpha (cdot ),lambda }({mathbb {R}}^n))</span>, respectively.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507720","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
p-adic Bessel $$alpha $$ -potentials and some of their applications p-adic Bessel $$alpha $$ -potentials 及其部分应用
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-06-22 DOI: 10.1007/s11868-024-00613-2
Anselmo Torresblanca-Badillo, J. E. Ospino, Francisco Arias
{"title":"p-adic Bessel $$alpha $$ -potentials and some of their applications","authors":"Anselmo Torresblanca-Badillo, J. E. Ospino, Francisco Arias","doi":"10.1007/s11868-024-00613-2","DOIUrl":"https://doi.org/10.1007/s11868-024-00613-2","url":null,"abstract":"<p>In this article, we will study a class of pseudo-differential operators on <i>p</i>-adic numbers, which we will call <i>p</i>-adic Bessel <span>(alpha )</span>-potentials. These operators are denoted and defined in the form </p><span>$$begin{aligned} (mathcal {E}_{varvec{phi },alpha }f)(x)=-mathcal {F}^{-1}_{zeta rightarrow x}left( left[ max {1,|varvec{phi }(||zeta ||_{p})|} right] ^{-alpha }widehat{f}(zeta )right) , text { } xin {mathbb {Q}}_{p}^{n}, alpha in mathbb {R}, end{aligned}$$</span><p>where <i>f</i> is a <i>p</i>-adic distribution and <span>(left[ max {1,|varvec{phi }(||zeta ||_{p})|}right] ^{-alpha })</span> is the symbol of the operator. We will study some properties of the convolution kernel (denoted as <span>(K_{alpha })</span>) of the pseudo-differential operator <span>(mathcal {E}_{varvec{phi },alpha })</span>, <span>(alpha in mathbb {R})</span>; and demonstrate that the family <span>((K_{alpha })_{alpha &gt;0})</span> determines a convolution semigroup on <span>(mathbb {Q}_{p}^{n})</span>. Furthermore, we will introduce new types of Feller semigroups, and explore new Markov processes and non-homogeneous initial value problems on <i>p</i>-adic numbers.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"183 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507721","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
The Hartley–Bessel function: product formula and convolution structure 哈特里-贝塞尔函数：乘积公式和卷积结构
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-05-07 DOI: 10.1007/s11868-024-00610-5
F. Bouzeffour
{"title":"The Hartley–Bessel function: product formula and convolution structure","authors":"F. Bouzeffour","doi":"10.1007/s11868-024-00610-5","DOIUrl":"https://doi.org/10.1007/s11868-024-00610-5","url":null,"abstract":"<p>This paper explores a one-parameter extension of the Hartley kernel expressed as a real combination of two Bessel functions, termed the Hartley–Bessel function. The key feature of the Hartley–Bessel function is derived through a limit transition from the <span>(-1)</span> little Jacobi polynomials. The Hartley–Bessel function emerges as an eigenfunction of a first-order difference-differential operator and possesses a Sonin integral-type representation. Our main contribution lies in investigating anovel product formula for this function, which subsequently facilitates the development of innovative generalized translation and convolution structures on the real line. The obtained product formula is expressed as an integral in terms of this function with an explicit non-positive and uniformly bounded measure. Consequently, a non-positivity-preserving convolution structure is established.\u0000</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"15 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888010","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
Quasinormable Fréchet spaces and M. W. Wong’s inequality 类非线性弗雷谢特空间和 M. W. Wong 不等式
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-05-03 DOI: 10.1007/s11868-024-00606-1
Eduard A. Nigsch, Norbert Ortner
{"title":"Quasinormable Fréchet spaces and M. W. Wong’s inequality","authors":"Eduard A. Nigsch, Norbert Ortner","doi":"10.1007/s11868-024-00606-1","DOIUrl":"https://doi.org/10.1007/s11868-024-00606-1","url":null,"abstract":"<p>A short proof of M. W. Wong’s inequality <span>(leftVert J_{-s}varphi rightVert _p le varepsilon leftVert J_{-t}varphi rightVert _p + C leftVert varphi rightVert _p)</span> is given.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"72 5 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881441","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
The general Dabrowski–Sitarz–Zalecki type theorem for odd dimensional manifolds with boundary III 有边界奇维流形的一般达布罗夫斯基-西塔尔兹-扎莱基类型定理 III
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-05-03 DOI: 10.1007/s11868-024-00604-3
Yuchen Yang, Yong Wang
{"title":"The general Dabrowski–Sitarz–Zalecki type theorem for odd dimensional manifolds with boundary III","authors":"Yuchen Yang, Yong Wang","doi":"10.1007/s11868-024-00604-3","DOIUrl":"https://doi.org/10.1007/s11868-024-00604-3","url":null,"abstract":"<p>In this paper, for the Dirac operator and three One-forms we give the proof of the another general Dabrowski–Sitarz–Zalecki type theorem for the spectral Einstein functional on odd dimensional manifolds with boundary.\u0000</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"58 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888125","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
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