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Two-weight norm inequalities for Hardy operators in generalized Morrey spaces 广义Morrey空间中Hardy算子的双权范数不等式
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-05 DOI: 10.1007/s13324-026-01240-4
Natasha Samko
{"title":"Two-weight norm inequalities for Hardy operators in generalized Morrey spaces","authors":"Natasha Samko","doi":"10.1007/s13324-026-01240-4","DOIUrl":"10.1007/s13324-026-01240-4","url":null,"abstract":"<div><p>We introduce the classes <span>(B_{p,q} (varphi , psi ))</span> and <span>(mathcal {B}_{p,q} (varphi , psi ))</span> of pairs (<i>u</i>, <i>v</i>) of weights <i>u</i> and <i>v</i> on <span>(mathbb {R}^n)</span> and prove two-weight norm estimates between two local generalized Morrey spaces for the multi-dimensional Hardy operator and its adjoint for weights in these classes. Such estimates were earlier known in the one-weight case and for radial weights. The proof is based on point-wise estimates for the Hardy operator and its adjoint via the norm of the domain space. A number of theorems on inclusion of pairs of radial weights into the classed <span>(B_{p,q} (varphi , psi ))</span> and <span>(mathcal {B}_{p,q} (varphi , psi ))</span> is proved. Belonging of pairs of weights to the introduced classes proves to have a form of criterion for two-weight norm estimates in the case of classical Morrey spaces and power weights. We also apply the obtained results to two-weight study of multidimensional versions of Calderón and Stieltjes operators in Morrey spaces.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01240-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750880","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
Two-weight norm inequalities for Hardy operators in generalized Morrey spaces 广义Morrey空间中Hardy算子的双权范数不等式
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-05 DOI: 10.1007/s13324-026-01240-4
Natasha Samko
{"title":"Two-weight norm inequalities for Hardy operators in generalized Morrey spaces","authors":"Natasha Samko","doi":"10.1007/s13324-026-01240-4","DOIUrl":"10.1007/s13324-026-01240-4","url":null,"abstract":"<div><p>We introduce the classes <span>(B_{p,q} (varphi , psi ))</span> and <span>(mathcal {B}_{p,q} (varphi , psi ))</span> of pairs (<i>u</i>, <i>v</i>) of weights <i>u</i> and <i>v</i> on <span>(mathbb {R}^n)</span> and prove two-weight norm estimates between two local generalized Morrey spaces for the multi-dimensional Hardy operator and its adjoint for weights in these classes. Such estimates were earlier known in the one-weight case and for radial weights. The proof is based on point-wise estimates for the Hardy operator and its adjoint via the norm of the domain space. A number of theorems on inclusion of pairs of radial weights into the classed <span>(B_{p,q} (varphi , psi ))</span> and <span>(mathcal {B}_{p,q} (varphi , psi ))</span> is proved. Belonging of pairs of weights to the introduced classes proves to have a form of criterion for two-weight norm estimates in the case of classical Morrey spaces and power weights. We also apply the obtained results to two-weight study of multidimensional versions of Calderón and Stieltjes operators in Morrey spaces.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01240-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750878","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
Quasiperiodic inverse Sturm-Liouville problem 拟周期逆Sturm-Liouville问题
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-05 DOI: 10.1007/s13324-026-01253-z
Natalia P. Bondarenko
{"title":"Quasiperiodic inverse Sturm-Liouville problem","authors":"Natalia P. Bondarenko","doi":"10.1007/s13324-026-01253-z","DOIUrl":"10.1007/s13324-026-01253-z","url":null,"abstract":"<div><p>In this paper, the Sturm-Liouville problem with nonseparated quasiperiodic boundary conditions is considered. We study the recovery of the problem parameters from the Hill-type discriminant, the Dirichlet spectrum, and the sequence of signs. We obtain the necessary and sufficient conditions of solvability, the local solvability and stability, as well as the uniform stability for this inverse spectral problem.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750877","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
Finite time blow-up for the semilinear parabolic equation with a memory term 具有记忆项的半线性抛物方程的有限时间爆破
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-04 DOI: 10.1007/s13324-026-01254-y
Kailun Wang, Guangyu Xu, Hong Yi
{"title":"Finite time blow-up for the semilinear parabolic equation with a memory term","authors":"Kailun Wang,&nbsp;Guangyu Xu,&nbsp;Hong Yi","doi":"10.1007/s13324-026-01254-y","DOIUrl":"10.1007/s13324-026-01254-y","url":null,"abstract":"<div><p>This paper is devoted to the study of finite time blow-up for initial-boundary value problem to a class of semilinear parabolic equation under the influence of a linear memory term </p><div><div><span>$$begin{aligned} displaystyle u_{t}-Delta u+int _{0}^{t}g(t-s)Delta u(x,s)ds =|u|^{p-2}u,quad text{ in } Omega times (0, T), end{aligned}$$</span></div></div><p>where parameter <span>(p&gt;2)</span> and <span>(Omega )</span> is a smooth bounded domain in <span>(mathbb {R}^{n}, nge 1, Tin (0, infty ])</span> is the maximal existence time of solution. By virtue of the concavity method, variational method, an improved potential well method involving time variable <i>t</i> and some new differential inequality techniques, we obtain three finite time blow-up results for the problem under different initial energy levels and suitably assumptions on the relaxation function <i>g</i>, we also derive the upper bound estimation for the blow-up time. Regarding the hypotheses on initial data and function <i>g</i>, our findings improve several existing finite time blow-up conclusions.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667115","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
Finite time blow-up for the semilinear parabolic equation with a memory term 具有记忆项的半线性抛物方程的有限时间爆破
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-04 DOI: 10.1007/s13324-026-01254-y
Kailun Wang, Guangyu Xu, Hong Yi
{"title":"Finite time blow-up for the semilinear parabolic equation with a memory term","authors":"Kailun Wang,&nbsp;Guangyu Xu,&nbsp;Hong Yi","doi":"10.1007/s13324-026-01254-y","DOIUrl":"10.1007/s13324-026-01254-y","url":null,"abstract":"<div><p>This paper is devoted to the study of finite time blow-up for initial-boundary value problem to a class of semilinear parabolic equation under the influence of a linear memory term </p><div><div><span>$$begin{aligned} displaystyle u_{t}-Delta u+int _{0}^{t}g(t-s)Delta u(x,s)ds =|u|^{p-2}u,quad text{ in } Omega times (0, T), end{aligned}$$</span></div></div><p>where parameter <span>(p&gt;2)</span> and <span>(Omega )</span> is a smooth bounded domain in <span>(mathbb {R}^{n}, nge 1, Tin (0, infty ])</span> is the maximal existence time of solution. By virtue of the concavity method, variational method, an improved potential well method involving time variable <i>t</i> and some new differential inequality techniques, we obtain three finite time blow-up results for the problem under different initial energy levels and suitably assumptions on the relaxation function <i>g</i>, we also derive the upper bound estimation for the blow-up time. Regarding the hypotheses on initial data and function <i>g</i>, our findings improve several existing finite time blow-up conclusions.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667114","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
Finite-support admissibility and Hausdorff interface geometry 有限支持容许度与Hausdorff界面几何
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-08-01 DOI: 10.1007/s13324-026-01250-2
Calvin A. Grant
{"title":"Finite-support admissibility and Hausdorff interface geometry","authors":"Calvin A. Grant","doi":"10.1007/s13324-026-01250-2","DOIUrl":"10.1007/s13324-026-01250-2","url":null,"abstract":"<div><p>We construct a finite-support geometric framework in which electromagnetic coupling arises as the affine projection of an admissible interface geometry. The underlying structure is defined by a local admissibility partition on sign-chains of an ordering field, yielding a spectrum with eigenvalues <span>(lambda _{textrm{adm}})</span> and <span>(lambda _{textrm{res}} = 1 - lambda _{textrm{adm}})</span>. For the electromagnetic channel, this spectrum is fixed by admissibility to <span>(lambda _{textrm{adm}} = 2/3)</span> and <span>(lambda _{textrm{res}} = 1/3)</span>. We show that the electromagnetic interface has intrinsic Hausdorff dimension <span>(D_H^{textrm{EM}} = 1 + lambda _{textrm{res}} = 4/3)</span>, and that the low-energy coupling is the Hausdorff density of this interface under inverse-power smoothing at the Thomson scale: </p><div><div><span>$$begin{aligned} alpha (mu _0) = frac{1}{4pi },mu _0^{-1/3},mathcal {H}^{4/3}!left( mathcal {L}_infty ^{textrm{EM}}right) . end{aligned}$$</span></div></div><p>The scale evolution of the coupling follows from the same admissibility spectrum: </p><div><div><span>$$begin{aligned} frac{dalpha }{dln mu } = frac{alpha ^2}{2pi },lambda _{textrm{adm}}sum _f Q_f^2, end{aligned}$$</span></div></div><p>with <span>(lambda _{textrm{adm}} = 2/3)</span> for the electromagnetic channel. Both the geometric scaling and the coupling structure are determined by a single admissibility partition. Conventional electromagnetic expressions arise as affine readouts of this finite-support geometry.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628665","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
Symmetrization of measures and the one-dimensional Poisson equation with Dirichlet boundary conditions 测度的对称性与Dirichlet边界条件下的一维泊松方程
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-07-31 DOI: 10.1007/s13324-026-01249-9
Christos Papadimitriou
{"title":"Symmetrization of measures and the one-dimensional Poisson equation with Dirichlet boundary conditions","authors":"Christos Papadimitriou","doi":"10.1007/s13324-026-01249-9","DOIUrl":"10.1007/s13324-026-01249-9","url":null,"abstract":"<div><p>Let <span>(mu )</span> be a finite Borel measure on <span>((-pi ,pi ))</span>. Consider the one-dimensional Poisson equation <span>(-u''=mu )</span>, where equality holds in the sense of distributions, with Dirichlet boundary conditions <span>(u(pm pi )=0)</span>. In this paper, we define measures that are transformations of <span>(mu )</span>, we compare the convex integral means of the original solutions <span>(u_mu )</span> and the transformed ones, and we prove the uniqueness of a solution that maximizes the convex integral means.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628602","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
Viscosity solutions in Martinet spaces 马丁内空间的粘度解
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-07-31 DOI: 10.1007/s13324-026-01251-1
Thomas Bieske, Frederic Bowen
{"title":"Viscosity solutions in Martinet spaces","authors":"Thomas Bieske,&nbsp;Frederic Bowen","doi":"10.1007/s13324-026-01251-1","DOIUrl":"10.1007/s13324-026-01251-1","url":null,"abstract":"<div><p>In this paper, we establish the properties of viscosity solutions in Martinet spaces, which are sub-Riemannian spaces that lack both the algebraic group law of Carnot groups and the triangular vector fields of Grushin-type spaces. We then prove the uniqueness of viscosity solutions to strictly monotone elliptic PDEs, to the infinite Laplace equation, and to the <span>({mathbf {infty (x)}})</span>-Laplace equation.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01251-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628524","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
Weyl-function asymptotics with applications to (mathcal{P}mathcal{T})-symmetry and point interactions weyl函数渐近与(mathcal{P}mathcal{T}) -对称和点相互作用的应用
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-07-25 DOI: 10.1007/s13324-026-01245-z
Marco Marletta, Iveta Semorádová
{"title":"Weyl-function asymptotics with applications to (mathcal{P}mathcal{T})-symmetry and point interactions","authors":"Marco Marletta,&nbsp;Iveta Semorádová","doi":"10.1007/s13324-026-01245-z","DOIUrl":"10.1007/s13324-026-01245-z","url":null,"abstract":"<div><p>Weyl <i>m</i>-function characterisations can be used to describe the behaviour of eigenvalues of Schrödinger operators with point interactions. Using complex scaling, transformators and a local Borg-Marchenko theorem we describe the asymptotic behaviour of <span>(m(lambda ))</span> as <span>(|lambda |rightarrow infty )</span> in different regions of <span>(mathbb {C})</span>. Our asymptotic results are applied to the evolution of real eigenvalues of <span>(delta )</span> and <span>(delta ')</span> perturbations of <span>(mathcal{P}mathcal{T})</span>-symmetric problems as functions of coupling constants.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01245-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614501","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
Anderson localization on quantum graphs coded by elements of a subshift of finite type 有限型子移元素编码的量子图上的安德森定位
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-07-24 DOI: 10.1007/s13324-026-01246-y
Oleg Safronov
{"title":"Anderson localization on quantum graphs coded by elements of a subshift of finite type","authors":"Oleg Safronov","doi":"10.1007/s13324-026-01246-y","DOIUrl":"10.1007/s13324-026-01246-y","url":null,"abstract":"<div><p>We study Schrödinger operators on quantum graphs where the number of edges between points is determined by orbits of a \"shift of finite type\". We prove Anderson localization for these systems.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01246-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614343","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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