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Grand Besov–Bourgain–Morrey spaces and their applications to boundedness of operators 大贝索夫-布尔干姆雷空间及其在算子有界性中的应用
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-06-20 DOI: 10.1007/s13324-024-00932-z
Yijin Zhang, Dachun Yang, Yirui Zhao
{"title":"Grand Besov–Bourgain–Morrey spaces and their applications to boundedness of operators","authors":"Yijin Zhang,&nbsp;Dachun Yang,&nbsp;Yirui Zhao","doi":"10.1007/s13324-024-00932-z","DOIUrl":"10.1007/s13324-024-00932-z","url":null,"abstract":"<div><p>Let <span>(1&lt;qle p le rle infty )</span> and <span>(tau in (0,infty ])</span>. Besov–Bourgain–Morrey spaces <span>({mathcal {M}}dot{B}^{p,tau }_{q,r}({mathbb {R}}^n))</span> in the special case where <span>(tau =r)</span>, extending what was introduced by J. Bourgain, have proved useful in the study related to the Strichartz estimate and the non-linear Schrödinger equation. In this article, by cleverly mixing the norm structures of grand Lebesgue spaces and Besov–Bourgain–Morrey spaces and adding an extra exponent <span>(theta in [0,infty ))</span>, the authors introduce a new class of function spaces, called generalized grand Besov–Bourgain–Morrey spaces <span>({mathcal {M}}dot{B}^{p,tau }_{q),r,theta }({mathbb {R}}^n))</span>. The authors explore their various real-variable properties including pre-dual spaces and the Gagliardo–Peetre and the ± interpolation theorems. Via establishing some equivalent quasi-norms of <span>({mathcal {M}}dot{B}^{p,tau }_{q),r,theta }({mathbb {R}}^n))</span> related to Muckenhoupt <span>(A_1({mathbb {R}}^n))</span>-weights, the authors then obtain an extrapolation theorem of <span>({mathcal {M}}dot{B}^{p,tau }_{q),r,theta }({mathbb {R}}^n))</span>. Applying this extrapolation theorem, the Calderón product, and the sparse family of dyadic grids of <span>({mathbb {R}}^n)</span>, the authors establish the sharp boundedness on <span>({mathcal {M}}dot{B}^{p,tau }_{q),r,theta }({mathbb {R}}^n))</span> of the Hardy–Littlewood maximal operator, the fractional integral, and the Calderón–Zygmund operator.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529458","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 and regularity of capacity solutions for a strongly coupled system derived from a thermistor problem 热敏电阻问题衍生的强耦合系统容量解的存在性和正则性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-06-15 DOI: 10.1007/s13324-024-00940-z
Rabab Elarabi
{"title":"Existence and regularity of capacity solutions for a strongly coupled system derived from a thermistor problem","authors":"Rabab Elarabi","doi":"10.1007/s13324-024-00940-z","DOIUrl":"10.1007/s13324-024-00940-z","url":null,"abstract":"<div><p>This paper explores strongly parabolic-elliptic systems within Orlicz–Sobolev spaces. It introduces the concept of capacity solutions and emphasizes the establishment of existence and regularity of solutions through rigorous proofs. Specifically, it addresses the existence of capacity solutions for a strongly nonlinear coupled system without reliance on the <span>(Delta _2)</span>-condition for the N-function. This system, akin to a modified thermistor problem, concerns the determination of variables representing the temperature within a conductor and the associated electrical potential.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141336615","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
Coercive inequalities on Carnot groups: taming singularities 卡诺群上的强制不等式：驯服奇点
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-06-12 DOI: 10.1007/s13324-024-00908-z
E. Bou Dagher, B. Zegarliński
{"title":"Coercive inequalities on Carnot groups: taming singularities","authors":"E. Bou Dagher,&nbsp;B. Zegarliński","doi":"10.1007/s13324-024-00908-z","DOIUrl":"10.1007/s13324-024-00908-z","url":null,"abstract":"<div><p>In the setting of Carnot groups, we propose an approach of taming singularities to get coercive inequalities. To this end, we develop a technique to introduce natural singularities in the energy function <i>U</i> in order to force one of the coercivity conditions. In particular, we explore explicit constructions of probability measures on Carnot groups which secure Poincaré and even Logarithmic Sobolev inequalities. As applications, we get analogues of the Dyson–Ornstein–Uhlenbeck model on the Heisenberg group and obtain results on the discreteness of the spectrum of related Markov generators.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00908-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506715","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
Spectral properties of Sturm–Liouville operators on infinite metric graphs 无限度量图上 Sturm-Liouville 算子的谱特性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-06-11 DOI: 10.1007/s13324-024-00937-8
Yihan Liu, Jun Yan, Jia Zhao
{"title":"Spectral properties of Sturm–Liouville operators on infinite metric graphs","authors":"Yihan Liu,&nbsp;Jun Yan,&nbsp;Jia Zhao","doi":"10.1007/s13324-024-00937-8","DOIUrl":"10.1007/s13324-024-00937-8","url":null,"abstract":"<div><p>This paper mainly deals with the Sturm–Liouville operator </p><div><div><span>$$begin{aligned} textbf{H}=frac{1}{w(x)}left( -frac{textrm{d}}{textrm{d}x}p(x)frac{ textrm{d}}{textrm{d}x}+q(x)right) ,text { }xin Gamma end{aligned}$$</span></div></div><p>acting in <span>(L_{w}^{2}left( Gamma right) ,)</span> where <span>(Gamma )</span> is a metric graph. We establish a relationship between the bottom of the spectrum and the positive solutions of quantum graphs, which is a generalization of the classical Allegretto–Piepenbrink theorem. Moreover, we prove the Persson-type theorem, which characterizes the infimum of the essential spectrum.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506716","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
Asymptotic isospectrality of Schrödinger operators on periodic graphs 周期图上薛定谔算子的渐近等谱性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-06-08 DOI: 10.1007/s13324-024-00938-7
Natalia Saburova
{"title":"Asymptotic isospectrality of Schrödinger operators on periodic graphs","authors":"Natalia Saburova","doi":"10.1007/s13324-024-00938-7","DOIUrl":"10.1007/s13324-024-00938-7","url":null,"abstract":"<div><p>We consider discrete Schrödinger operators with periodic potentials on periodic graphs. Their spectra consist of a finite number of bands. We perturb a periodic graph by adding edges in a periodic way (without changing the vertex set) and show that if the added edges are long enough, then the perturbed graph is asymptotically isospectral to some periodic graph of a higher dimension but without long edges. We also obtain a criterion for the perturbed graph to be not only asymptotically isospectral but just isospectral to this higher dimensional periodic graph. One of the simplest examples of such asymptotically isospectral periodic graphs is the square lattice perturbed by long edges and the cubic lattice. We also get asymptotics of the endpoints of the spectral bands for the Schrödinger operator on the perturbed graph as the length of the added edges tends to infinity.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506717","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
Preimages under linear combinations of iterates of finite Blaschke products 有限布拉什克积迭代的线性组合下的预成像
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-06-06 DOI: 10.1007/s13324-024-00907-0
Spyridon Kakaroumpas, Odí Soler i Gibert
{"title":"Preimages under linear combinations of iterates of finite Blaschke products","authors":"Spyridon Kakaroumpas,&nbsp;Odí Soler i Gibert","doi":"10.1007/s13324-024-00907-0","DOIUrl":"10.1007/s13324-024-00907-0","url":null,"abstract":"<div><p>Consider a finite Blaschke product <i>f</i> with <span>(f(0) = 0)</span> which is not a rotation and denote by <span>(f^n)</span> its <i>n</i>-th iterate. Given a sequence <span>({a_n})</span> of complex numbers, consider the series <span>(F(z) = sum _n a_n f^n(z).)</span> We show that for any <span>(w in mathbb {C},)</span> if <span>({a_n})</span> tends to zero but <span>(sum _n |a_n| = infty ,)</span> then the set of points <span>(xi )</span> in the unit circle for which the series <span>(F(xi ))</span> converges to <i>w</i> has Hausdorff dimension 1. Moreover, we prove that this result is optimal in the sense that the conclusion does not hold in general if one considers Hausdorff measures given by any measure function more restrictive than the power functions <span>(t^delta ,)</span> <span>(0&lt; delta &lt; 1.)</span></p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141410319","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 estimates of commutators of singular operators in generalized Morrey spaces beyond Muckenhoupt range and applications 超越穆肯霍普特范围的广义莫雷空间奇异算子换向器的加权估计及其应用
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-05-30 DOI: 10.1007/s13324-024-00934-x
Natasha Samko
{"title":"Weighted estimates of commutators of singular operators in generalized Morrey spaces beyond Muckenhoupt range and applications","authors":"Natasha Samko","doi":"10.1007/s13324-024-00934-x","DOIUrl":"10.1007/s13324-024-00934-x","url":null,"abstract":"<div><p>For a certain class of radial weights, we prove weighted norm estimates for commutators with BMO coefficients of singular operators in local generalized Morrey spaces. As a consequence of these estimates, we obtain norm inequalities for such commutators in the generalized Stummel-Morrey spaces. We also discuss a.e. well-posedness of singular operators and their commutators on weighted generalized Morrey spaces. The obtained estimates are applied to prove interior regularity for solutions of elliptic PDEs in the frameworks of the corresponding weighted Sobolev spaces based on the local generalized Morrey spaces or Stummel-Morrey spaces. To this end also conditions for the applicability of the representation formula, for the second-order derivatives of solutions to elliptic PDEs, are found for the case of such weighted spaces. In both results, for commutators and applications, we admit weights beyond the Muckenhoupt range.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00934-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189282","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
Monotonicity of solutions to degenerate p-Laplace problems with a gradient term in half-spaces 半空间中有梯度项的退化 p 拉普拉斯问题解的单调性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-05-25 DOI: 10.1007/s13324-024-00933-y
Phuong Le, Nhat Vy Huynh
{"title":"Monotonicity of solutions to degenerate p-Laplace problems with a gradient term in half-spaces","authors":"Phuong Le,&nbsp;Nhat Vy Huynh","doi":"10.1007/s13324-024-00933-y","DOIUrl":"10.1007/s13324-024-00933-y","url":null,"abstract":"<div><p>We establish the monotonicity of positive solutions to the problem </p><div><div><span>$$begin{aligned} -Delta _p u + a(u)|nabla u|^q = f(u) text { in } mathbb {R}^N_+, quad u=0 text { on } partial mathbb {R}^N_+, end{aligned}$$</span></div></div><p>where <span>(p&gt;2)</span>, <span>(qge p-1)</span> and <i>a</i>, <i>f</i> are locally Lipschitz continuous functions such that <i>f</i> is positive on <span>((0,+infty ))</span> and it is either sublinear or superlinear near 0. The main tool we use is the refined method of moving planes for quasilinear elliptic problems in half-spaces.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141098392","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 forward and backward shift on the Hardy space of a tree 树的哈代空间的前移和后移
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1007/s13324-024-00931-0
Adán Ángeles-Romero, Rubén A. Martínez-Avendaño
{"title":"The forward and backward shift on the Hardy space of a tree","authors":"Adán Ángeles-Romero,&nbsp;Rubén A. Martínez-Avendaño","doi":"10.1007/s13324-024-00931-0","DOIUrl":"10.1007/s13324-024-00931-0","url":null,"abstract":"<div><p>In this paper we initiate the study of the forward and backward shifts on the discrete generalized Hardy space of a tree and the discrete generalized little Hardy space of a tree. In particular, we investigate when these shifts are bounded, find the norm of the shifts if they are bounded, characterize the trees in which they are an isometry, compute the spectrum in some concrete examples, and completely determine when they are hypercyclic.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151219","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
Correction: Feynman checkers: lattice quantum field theory with real time 更正：费曼跳棋：实时网格量子场论
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1007/s13324-024-00935-w
M. Skopenkov, A. Ustinov
{"title":"Correction: Feynman checkers: lattice quantum field theory with real time","authors":"M. Skopenkov,&nbsp;A. Ustinov","doi":"10.1007/s13324-024-00935-w","DOIUrl":"10.1007/s13324-024-00935-w","url":null,"abstract":"","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141100023","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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