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Weighted norm inequalities with one-dimensional Hardy-type operators involving suprema
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
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
Zygmund theorem for harmonic quasiregular mappings
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-03-05 DOI: 10.1007/s13324-025-01043-z
David Kalaj
{"title":"Zygmund theorem for harmonic quasiregular mappings","authors":"David Kalaj","doi":"10.1007/s13324-025-01043-z","DOIUrl":"10.1007/s13324-025-01043-z","url":null,"abstract":"<div><p>Let <span>(Kge 1)</span>. We prove Zygmund theorem for <span>(K-)</span>quasiregular harmonic mappings in the unit disk <span>(mathbb {D})</span> in the complex plane by providing a constant <i>C</i>(<i>K</i>) in the inequality </p><div><div><span>$$begin{aligned} Vert fVert _{1}le C(K)(1+Vert textrm{Re},(f)log ^+ |textrm{Re}, f|Vert _1), end{aligned}$$</span></div></div><p>provided that <span>(textrm{Im},f(0)=0)</span>. Moreover for a quasiregular harmonic mapping <span>(f=(f_1,dots , f_n))</span> defined in the unit ball <span>(mathbb {B}subset mathbb {R}^n)</span>, we prove the asymptotically sharp inequality </p><div><div><span>$$begin{aligned} Vert fVert _{1}-|f(0)|le (n-1)K^2(Vert f_1log f_1Vert _1- f_1(0)log f_1(0)), end{aligned}$$</span></div></div><p>when <span>(Krightarrow 1)</span>, provided that <span>(f_1)</span> is positive.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553937","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
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
Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-25 DOI: 10.1007/s13324-025-01030-4
Bingxiao Liu, Dominik Zielinski
{"title":"Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros","authors":"Bingxiao Liu,&nbsp;Dominik Zielinski","doi":"10.1007/s13324-025-01030-4","DOIUrl":"10.1007/s13324-025-01030-4","url":null,"abstract":"<div><p>We present an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of Gaussian holomorphic sections in the semi-classical limit, including the equidistribution, large deviation estimates, central limit theorem, and number variances.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01030-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143481211","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
Homogenization of convolution type semigroups in high contrast media
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-21 DOI: 10.1007/s13324-025-01034-0
Andrey Piatnitski, Elena Zhizhina
{"title":"Homogenization of convolution type semigroups in high contrast media","authors":"Andrey Piatnitski,&nbsp;Elena Zhizhina","doi":"10.1007/s13324-025-01034-0","DOIUrl":"10.1007/s13324-025-01034-0","url":null,"abstract":"<div><p>The paper deals with the asymptotic properties of semigroups associated with Markov jump processes in a high contrast periodic medium in <span>(mathbb {R}^d)</span>, <span>(dge 1)</span>. In order to study the limit behaviour of these semigroups we equip the corresponding Markov processes with an extra variable that characterizes the position of the process inside the period, and show that the limit dynamics of these two-component processes remains Markov. We describe the limit process and prove the convergence of the corresponding semigroups as well as the convergence in law of the extended processes in the path space. Since the components of the limit process are coupled, the dynamics of the first (spacial) component need not have a semigroup property. We derive the evolution equation with a memory term for the dynamics of this component of the limit process. We also discuss the construction of the limit semigroup in the <span>(L^2)</span> space and study the spectrum of its generator.</p></div>","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":"https://link.springer.com/content/pdf/10.1007/s13324-025-01034-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455691","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
Retraction Note: Normal functions and products of spherical derivatives
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
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
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
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