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Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in ( {mathbf {mathbb {R}}}^{3} ) 二阶张量场的受限混合射线变换的微局部反演 ( {mathbf {mathbb {R}}}^{3} )
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-13 DOI: 10.1007/s13324-025-01044-y
Chandni Thakkar
{"title":"Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in ( {mathbf {mathbb {R}}}^{3} )","authors":"Chandni Thakkar","doi":"10.1007/s13324-025-01044-y","DOIUrl":"10.1007/s13324-025-01044-y","url":null,"abstract":"<div><p>In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray transform is restricted over lines passing through a fixed curve <span>(gamma )</span> in <span>(mathbb {R}^3)</span> satisfying certain geometric conditions. The main theorem of the article shows that a second-order tensor field can be recovered from its restricted mixed-ray transform up to the kernel of the transform, a smoothing term, and a known singular term.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143602322","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 existence and prolongation of infinitesimal isometries on special sub-Riemannian manifolds 特殊次黎曼流形上无限小等距的存在性与扩展
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-06 DOI: 10.1007/s13324-025-01035-z
Marek Grochowski
{"title":"On the existence and prolongation of infinitesimal isometries on special sub-Riemannian manifolds","authors":"Marek Grochowski","doi":"10.1007/s13324-025-01035-z","DOIUrl":"10.1007/s13324-025-01035-z","url":null,"abstract":"<div><p>In the present paper we deal with (local) infinitesimal isometries of special sub-Riemannian manifolds (a contact and oriented sub-Riemannian manifold is called special if the Reeb vector field is an infinitesimal isometry). The objective of the paper is to find some conditions on such manifolds which allow one to construct, locally around a given point, infinitesimal isometries and then, if possible, to prolong them onto bigger domains. The mentioned conditions are related to the so-called <span>(mathfrak {i}^*)</span>-regular and <span>(mathfrak {i})</span>-regular points, the notions introduced by Nomizu (Ann Math 2:105–120, 1960) in the Riemannian setting and slightly modified by the author.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553781","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
Weighted norm inequalities with one-dimensional Hardy-type operators involving suprema 涉及上域的一维hardy型算子的加权范数不等式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-06 DOI: 10.1007/s13324-025-01041-1
Vladimir D. Stepanov
{"title":"Weighted norm inequalities with one-dimensional Hardy-type operators involving suprema","authors":"Vladimir D. Stepanov","doi":"10.1007/s13324-025-01041-1","DOIUrl":"10.1007/s13324-025-01041-1","url":null,"abstract":"<div><p>In this paper we obtain necessary and sufficient conditions for the boundedness in weighted Lebesgue spaces of one-dimensional Hardy-type operators involving suprema. In particular, we solve the problems from Frank RL (J. Math. Sci. 263:323-342, 2022)</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564453","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 solutions of some nonlocal models for nonlinear dispersive waves 非线性色散波的非局部模型解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-06 DOI: 10.1007/s13324-025-01042-0
Ailton C. Nascimento
{"title":"On the solutions of some nonlocal models for nonlinear dispersive waves","authors":"Ailton C. Nascimento","doi":"10.1007/s13324-025-01042-0","DOIUrl":"10.1007/s13324-025-01042-0","url":null,"abstract":"<div><p>In this paper we study special properties of solutions of the initial value problem associated to a class of nonlinear dispersive equations where the operator modelling dispersive effects is nonlocal. In particular, we prove that solutions of the surface tension Whitham equations posed on the real line satisfy the propagation of regularity phenomena, which says that regularity of the initial data on the right hand side of the real line is propagated to the left hand side by the flow solution. A similar result is obtained for solutions of the Full Dispersion Kadomtsev–Petviashvili equation, a natural (weakly transverse) two-dimensional version of the Whitham equation, with and without surface tension. We establish that the augmented regularity of the initial data on certain distinguished subsets of the Euclidean space is transmitted by the flow solution at an infinite rate. The underlying approach involves treating the general equation as a perturbed version of a class of fractional equations with well-established properties.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564454","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
Mixed radial-angular integrabilities for commutators of fractional Hardy operators with rough kernels 具有粗糙核的分数哈代算子换元的混合径向-角向积分性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-27 DOI: 10.1007/s13324-025-01037-x
Ronghui Liu, Shuangping Tao, Huoxiong Wu
{"title":"Mixed radial-angular integrabilities for commutators of fractional Hardy operators with rough kernels","authors":"Ronghui Liu,&nbsp;Shuangping Tao,&nbsp;Huoxiong Wu","doi":"10.1007/s13324-025-01037-x","DOIUrl":"10.1007/s13324-025-01037-x","url":null,"abstract":"<div><p>This paper is devoted to studying the boundedness of commutators <span>(textrm{H}_{Omega ,beta }^b)</span> generated by the rough fractional Hardy operators <span>(textrm{H}_{Omega ,beta })</span> with the symbol <i>b</i> on the mixed radial-angular spaces. When <i>b</i> is a mixed radial-angular central bounded mean oscillation function and <span>(Omega in L^s(S^{n-1}))</span> for some <span>(s&gt;1)</span>, the boundedness of <span>(textrm{H}_{Omega ,beta }^b)</span> on the mixed radial-angular homogeneous Herz spaces is established. Meanwhile, the boundedness for <span>(textrm{H}_{Omega ,beta }^b)</span> on the mixed radial-angular homogeneous <span>(lambda )</span>-central Morrey spaces is also obtained, provided that <i>b</i> belongs to the mixed radial-angular homogeneous <span>(lambda )</span>-central bounded mean oscillation spaces and <span>(Omega in L^s(S^{n-1}))</span> for some <span>(s&gt;1)</span>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513230","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-Laplacian problem in a Riemannian manifold 黎曼流形中的p-拉普拉斯问题
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-26 DOI: 10.1007/s13324-025-01031-3
J. Vanterler da C. Sousa, Lamine Mbarki, Leandro S. Tavares
{"title":"p-Laplacian problem in a Riemannian manifold","authors":"J. Vanterler da C. Sousa,&nbsp;Lamine Mbarki,&nbsp;Leandro S. Tavares","doi":"10.1007/s13324-025-01031-3","DOIUrl":"10.1007/s13324-025-01031-3","url":null,"abstract":"<div><p>This paper is divided into two parts. First, we will prove the existence of solutions of the <i>p</i>-Laplacian equation in the Riemannian manifold in the space <span>({mathcal {H}}^{alpha ,p}_{loc}({mathcal {N}}))</span>. On the other hand, we will give a criterion to obtain a positive lower bound for <span>(lambda _{1,p}(Omega ))</span>, where is a bounded domain <span>(Omega subset {mathcal {N}})</span>. In the first result, we do not consider a bounded subset on the Riemannian manifold <span>({mathcal {N}})</span>. \u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143496825","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
Retraction Note: Normal functions and products of spherical derivatives 注：正函数和球面导数的乘积
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-21 DOI: 10.1007/s13324-025-01040-2
Yan Xu, Huiling Qiu
{"title":"Retraction Note: Normal functions and products of spherical derivatives","authors":"Yan Xu,&nbsp;Huiling Qiu","doi":"10.1007/s13324-025-01040-2","DOIUrl":"10.1007/s13324-025-01040-2","url":null,"abstract":"","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465970","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
Blow-up of solutions to fractional quasilinear hyperbolic problem 分数阶拟线性双曲型问题解的爆破
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-20 DOI: 10.1007/s13324-025-01033-1
J. Vanterler da C. Sousa, D. S. Oliveira
{"title":"Blow-up of solutions to fractional quasilinear hyperbolic problem","authors":"J. Vanterler da C. Sousa,&nbsp;D. S. Oliveira","doi":"10.1007/s13324-025-01033-1","DOIUrl":"10.1007/s13324-025-01033-1","url":null,"abstract":"<div><p>In this paper, we consider blow-up solutions of a nonlinear hyperbolic fractional equation with variable exponents of nonlinearities in the fractional space <span>(mathcal {H}_{p(xi )}^{alpha }(Omega ))</span>. To achieve this, we introduce a control function and use energy inequalities to discuss various estimates. In this sense, we address the problem of non-existence of solutions and derive an estimate for the upper bound of the blow-up time. Finally, we provide classical theoretical insights into possible special cases of the results obtained in this study.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01033-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interpolation of variable Hardy–Lorentz–Karamata spaces associated with rearrangement functions 与重排函数相关的变量Hardy-Lorentz-Karamata空间的插值
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-20 DOI: 10.1007/s13324-025-01032-2
Zhiwei Hao, Libo Li, Ferenc Weisz
{"title":"Interpolation of variable Hardy–Lorentz–Karamata spaces associated with rearrangement functions","authors":"Zhiwei Hao,&nbsp;Libo Li,&nbsp;Ferenc Weisz","doi":"10.1007/s13324-025-01032-2","DOIUrl":"10.1007/s13324-025-01032-2","url":null,"abstract":"<div><p>In this article, we introduce variable Lorentz–Karamata spaces <span>({mathcal {L}}_{p(cdot ),q,b}(R))</span> defined by rearrangement functions and develop the martingale theory in this framework. The real interpolation theory for variable Lorentz–Karamata spaces is presented. Based on this and the new atomic decomposition, we study the real interpolation theory for variable martingale Hardy–Lorentz–Karamata spaces. We also characterize the real interpolation spaces between variable martingale Hardy spaces and <span>(BMO_2)</span> spaces. The results obtained here generalize the previous results for variable Lorentz spaces as well as for variable martingale Hardy–Lorentz spaces. Moreover, we remove the condition <span>(theta +p_-&gt;1)</span> in [Banach J. Math. Anal. 2023, 17(3): 47].</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01032-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse scattering problems for the Dirac operator on the line with partial knowledge of the potential 具有部分位势的直线上狄拉克算子的逆散射问题
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-13 DOI: 10.1007/s13324-025-01029-x
Ying Yang, Haiyan Jin, Guangsheng Wei
{"title":"Inverse scattering problems for the Dirac operator on the line with partial knowledge of the potential","authors":"Ying Yang,&nbsp;Haiyan Jin,&nbsp;Guangsheng Wei","doi":"10.1007/s13324-025-01029-x","DOIUrl":"10.1007/s13324-025-01029-x","url":null,"abstract":"<div><p>The inverse scattering problem for the Dirac equation on the real line are considered. It is shown that the potential on the real line is uniquely determined in terms of the mixed scattering data which consists of the knowledge of the potential on the right (left) half line of the real axis and the reflection coefficient from the right (left). In particular, neither the bound states or the bound state norming constants are needed. The method is based on a factorization of a scattering matrix.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396479","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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