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Revista Matemática Complutense最新文献

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$$A_p$$ weights on nonhomogeneous trees equipped with measures of exponential growth 配备指数增长措施的非均质树的 $$A_p$$ 权重
Revista Matemática Complutense Pub Date : 2024-09-17 DOI: 10.1007/s13163-024-00501-9
Alessandro Ottazzi, Federico Santagati, Maria Vallarino
{"title":"$$A_p$$ weights on nonhomogeneous trees equipped with measures of exponential growth","authors":"Alessandro Ottazzi, Federico Santagati, Maria Vallarino","doi":"10.1007/s13163-024-00501-9","DOIUrl":"https://doi.org/10.1007/s13163-024-00501-9","url":null,"abstract":"<p>This paper aims to study <span>(A_p)</span> weights in the context of a class of metric measure spaces with exponential volume growth, namely infinite trees with root at infinity equipped with the geodesic distance and flow measures. Our main result is a Muckenhoupt Theorem, which is a characterization of the weights for which a suitable Hardy–Littlewood maximal operator is bounded on the corresponding weighted <span>(L^p)</span> spaces. We emphasise that this result does not require any geometric assumption on the tree or any condition on the flow measure. We also prove a reverse Hölder inequality in the case when the flow measure is locally doubling. We finally show that the logarithm of an <span>(A_p)</span> weight is in BMO and discuss the connection between <span>(A_p)</span> weights and quasisymmetric mappings.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142247532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Revisited convexity notions for $$L^infty $$ variational problems 重新审视 $$L^infty$ 变分问题的凸性概念
Revista Matemática Complutense Pub Date : 2024-09-03 DOI: 10.1007/s13163-024-00499-0
Ana Margarida Ribeiro, Elvira Zappale
{"title":"Revisited convexity notions for $$L^infty $$ variational problems","authors":"Ana Margarida Ribeiro, Elvira Zappale","doi":"10.1007/s13163-024-00499-0","DOIUrl":"https://doi.org/10.1007/s13163-024-00499-0","url":null,"abstract":"<p>We address a detailed study of the convexity notions that arise in the study of weak* lower semicontinuity of supremal functionals, as well as those arising by the <span>(L^p)</span>-approximation, as <span>(p rightarrow +infty )</span> of such functionals. Our quest is motivated by the knowledge we have on the analogous integral functionals and aims at establishing a solid groundwork underlying further research in the <span>(L^infty )</span> context.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dispersiveness and controllability of invariant control systems on nilpotent Lie groups 零potent Lie 群上不变控制系统的分散性和可控性
Revista Matemática Complutense Pub Date : 2024-08-21 DOI: 10.1007/s13163-024-00500-w
Jean G. Silva, Josiney A. Souza
{"title":"Dispersiveness and controllability of invariant control systems on nilpotent Lie groups","authors":"Jean G. Silva, Josiney A. Souza","doi":"10.1007/s13163-024-00500-w","DOIUrl":"https://doi.org/10.1007/s13163-024-00500-w","url":null,"abstract":"<p>This manuscript presents sufficient conditions for dispersiveness of invariant control systems on nilpotent Lie groups. The main theorem shows that a nilpotent control system is dispersive if its drift vector is not a linear combination of the controlled vectors and the Lie brackets among all the vector fields of the system. This condition implies a necessary condition for the existence of a control set. A classification of homogeneous and inhomogeneous nilpotent control systems is presented.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Heuristic derivation of Zudilin’s supercongruences for rational Ramanujan series 有理拉曼奴扬级数的祖迪林超公差启发式推导
Revista Matemática Complutense Pub Date : 2024-07-31 DOI: 10.1007/s13163-024-00498-1
Jesús Guillera
{"title":"Heuristic derivation of Zudilin’s supercongruences for rational Ramanujan series","authors":"Jesús Guillera","doi":"10.1007/s13163-024-00498-1","DOIUrl":"https://doi.org/10.1007/s13163-024-00498-1","url":null,"abstract":"<p>We derive, using a heuristic method, a <i>p</i>-adic mate of bilateral Ramanujan series. It has (among other consequences) Zudilin’s supercongruences for rational Ramanujan series.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 phenomenon to the semilinear heat equation for unbounded Laplacians on graphs 图上无界拉普拉卡半线性热方程的胀大现象
Revista Matemática Complutense Pub Date : 2024-07-24 DOI: 10.1007/s13163-024-00497-2
Yong Lin, Shuang Liu, Yiting Wu
{"title":"Blow-up phenomenon to the semilinear heat equation for unbounded Laplacians on graphs","authors":"Yong Lin, Shuang Liu, Yiting Wu","doi":"10.1007/s13163-024-00497-2","DOIUrl":"https://doi.org/10.1007/s13163-024-00497-2","url":null,"abstract":"<p>Let <span>(G=(V,E))</span> be an infinite graph. The purpose of this paper is to investigate the nonexistence of global solutions for the following semilinear heat equation </p><span>$$begin{aligned} left{ begin{array}{lc} partial _t u=Delta u + u^{1+alpha }, &amp;{}, t&gt;0,xin V, u(0,x)=u_0(x), &amp;{}, x in V, end{array} right. end{aligned}$$</span><p>where <span>(Delta )</span> is an unbounded Laplacian on <i>G</i>, <span>(alpha )</span> is a positive parameter and <span>(u_0)</span> is a nonnegative and nontrivial initial value. Using on-diagonal lower heat kernel bounds, we prove that the semilinear heat equation admits the blow-up solutions, which is viewed as a discrete analog of that of Fujita (J Fac Sci Univ Tokyo 13:109–124, 1966) and had been generalized to locally finite graphs with bounded Laplacians by Lin and Wu (Calc Var Partial Diff Equ 56(4):22, 2017). In this paper, new techniques have been developed to deal with unbounded graph Laplacians.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141773825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-dimensional Jacobians $$textrm{det}hspace{0.56905pt}$$ and $$textrm{Det}hspace{0.56905pt}$$ for bounded variation functions and applications 有界变化函数的二维雅各布数 $$textrm{det}hspace{0.56905pt}$$ 和 $$textrm{Det}hspace{0.56905pt}$ 及其应用
Revista Matemática Complutense Pub Date : 2024-07-14 DOI: 10.1007/s13163-024-00496-3
M. Briane, J. Casado-díaz
{"title":"Two-dimensional Jacobians $$textrm{det}hspace{0.56905pt}$$ and $$textrm{Det}hspace{0.56905pt}$$ for bounded variation functions and applications","authors":"M. Briane, J. Casado-díaz","doi":"10.1007/s13163-024-00496-3","DOIUrl":"https://doi.org/10.1007/s13163-024-00496-3","url":null,"abstract":"","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141650268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Littlewood–Paley–Stein square functions for the fractional discrete Laplacian on $$mathbb {Z}$$ $$mathbb {Z}$$ 上分数离散拉普拉斯函数的 Littlewood-Paley-Stein 平方函数
Revista Matemática Complutense Pub Date : 2024-06-18 DOI: 10.1007/s13163-024-00495-4
Huaiqian Li, Liying Mu
{"title":"Littlewood–Paley–Stein square functions for the fractional discrete Laplacian on $$mathbb {Z}$$","authors":"Huaiqian Li, Liying Mu","doi":"10.1007/s13163-024-00495-4","DOIUrl":"https://doi.org/10.1007/s13163-024-00495-4","url":null,"abstract":"<p>We investigate the boundedness of “vertical” Littlewood–Paley–Stein square functions for the nonlocal fractional discrete Laplacian on the lattice <span>(mathbb {Z})</span>, where the underlying graphs are not locally finite. When <span>(qin [2,infty ))</span>, we prove the <span>(l^q)</span> boundedness of the square function by exploring the corresponding Markov jump process and applying the martingale inequality. When <span>(qin (1,2])</span>, we consider a modified version of the square function and prove its <span>(l^q)</span> boundedness through a careful in on the generalized carré du champ operator. A counterexample is constructed to show that it is necessary to consider the modified version. Moreover, we extend the study to a class of nonlocal Schrödinger operators for <span>(qin (1,2])</span>.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Waldschmidt constant of a standard $$Bbbk $$ -configuration in $${mathbb P}^2$$ $${{mathbb P}^2$$ 中标准 $$Bbbk $$ 配置的沃尔德施密特常数
Revista Matemática Complutense Pub Date : 2024-06-18 DOI: 10.1007/s13163-024-00493-6
Maria Virginia Catalisano, Giuseppe Favacchio, Elena Guardo, Yong-Su Shin
{"title":"The Waldschmidt constant of a standard $$Bbbk $$ -configuration in $${mathbb P}^2$$","authors":"Maria Virginia Catalisano, Giuseppe Favacchio, Elena Guardo, Yong-Su Shin","doi":"10.1007/s13163-024-00493-6","DOIUrl":"https://doi.org/10.1007/s13163-024-00493-6","url":null,"abstract":"<p>A <span>(Bbbk )</span>-configuration of type <span>((d_1,ldots ,d_s))</span>, where <span>(1leqslant d_1&lt; cdots &lt; d_s )</span> are integers, is a set of points in <span>({mathbb P}^2)</span> that has a number of algebraic and geometric properties. For example, the graded Betti numbers and Hilbert functions of all <span>(Bbbk )</span>-configurations in <span>({mathbb P}^2)</span> are determined by the type <span>((d_1,ldots ,d_s))</span>. However the Waldschmidt constant of a <span>(Bbbk )</span>-configuration in <span>({mathbb P}^2)</span> of the same type may vary. In this paper, we find that the Waldschmidt constant of a <span>(Bbbk )</span>-configuration in <span>({mathbb P}^2)</span> of type <span>((d_1,ldots ,d_s))</span> with <span>(d_1ge sge 1)</span> is <i>s</i>. Then we deal with the Waldschmidt constants of standard <span>(Bbbk )</span>-configurations in <span>({mathbb P}^2)</span> of type (<i>a</i>), (<i>a</i>, <i>b</i>), and (<i>a</i>, <i>b</i>, <i>c</i>) with <span>(age 1)</span>. In particular, we prove that the Waldschmidt constant of a standard <span>(Bbbk )</span>-configuration in <span>({mathbb P}^2)</span> of type (1, <i>b</i>, <i>c</i>) with <span>(cge 2b+2)</span> does not depend on <i>c</i>.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum signal processing and nonlinear Fourier analysis 量子信号处理和非线性傅立叶分析
Revista Matemática Complutense Pub Date : 2024-06-14 DOI: 10.1007/s13163-024-00494-5
Michel Alexis, Gevorg Mnatsakanyan, Christoph Thiele
{"title":"Quantum signal processing and nonlinear Fourier analysis","authors":"Michel Alexis, Gevorg Mnatsakanyan, Christoph Thiele","doi":"10.1007/s13163-024-00494-5","DOIUrl":"https://doi.org/10.1007/s13163-024-00494-5","url":null,"abstract":"<p>Elucidating a connection with nonlinear Fourier analysis (NLFA), we extend a well known algorithm in quantum signal processing (QSP) to represent measurable signals by square summable sequences. Each coefficient of the sequence is Lipschitz continuous as a function of the signal.\u0000</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weighted weak-type inequalities for maximal operators and singular integrals 最大算子和奇异积分的加权弱型不等式
Revista Matemática Complutense Pub Date : 2024-05-18 DOI: 10.1007/s13163-024-00492-7
David Cruz-Uribe, Brandon Sweeting
{"title":"Weighted weak-type inequalities for maximal operators and singular integrals","authors":"David Cruz-Uribe, Brandon Sweeting","doi":"10.1007/s13163-024-00492-7","DOIUrl":"https://doi.org/10.1007/s13163-024-00492-7","url":null,"abstract":"<p>We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional integral operators. We consider a kind of weak-type inequality that was first studied by Muckenhoupt and Wheeden (Indiana Univ. Math. J. 26(5):801–816, 1977) and later in Cruz-Uribe et al. (Int. Math. Res. Not. 30:1849–1871, 2005). We obtain quantitative estimates for these operators in both the scalar and matrix weighted setting using sparse domination techniques. Our results extend those obtained by Cruz-Uribe et al. (Rev. Mat. Iberoam. 37(4):1513–1538, 2021) for singular integrals and maximal operators when <span>(p=1)</span>.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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