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Non-spectral problem of self-affine measures with consecutive collinear digits in (mathbb{R}^2) $$mathbb{R}^2$$中具有连续共线位数的自参量的非谱问题
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-18 DOI: 10.1007/s10476-024-00033-w
J. Su, S. Wu
{"title":"Non-spectral problem of self-affine measures with consecutive collinear digits in (mathbb{R}^2)","authors":"J. Su,&nbsp;S. Wu","doi":"10.1007/s10476-024-00033-w","DOIUrl":"10.1007/s10476-024-00033-w","url":null,"abstract":"<div><p>Let <span>(mu_{M,D})</span> be the planar self-affine measure generated by an expanding integer matrix <span>(Min M_2(mathbb{Z}))</span> and an integer digit set <span>(D={0,1,dots,q-1}v)</span> with <span>(vinmathbb{Z}^2setminus{0})</span>, where <span>(gcd(det(M),q)=1)</span> and <span>(qge 2)</span> is an integer. If the characteristic polynomial of <span>(M)</span> is <span>(f(x)=x^2+det(M))</span> and <span>({v, Mv})</span> is linearly independent, we show that there exist at most <span>(q^2)</span> mutually orthogonal exponential functions in <span>(L^2(mu_{M,D}))</span>, and the number <span>(q^2)</span> is the best. In particular, we further give a complete description for the case <span>(M= {rm diag}(s, t))</span>\u0000with <span>(gcd(st, q)=1)</span>. This extends the results of Wei and Zhang [24].\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"629 - 641"},"PeriodicalIF":0.6,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528956","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
Old and new Morrey spaces without heat kernel bounds on RD-spaces RD 空间上无热核边界的新旧莫雷空间
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-18 DOI: 10.1007/s10476-024-00026-9
Bo Li, Ba. Li, B. Ma, A. Wang, J. Li
{"title":"Old and new Morrey spaces without heat kernel bounds on RD-spaces","authors":"Bo Li,&nbsp;Ba. Li,&nbsp;B. Ma,&nbsp;A. Wang,&nbsp;J. Li","doi":"10.1007/s10476-024-00026-9","DOIUrl":"10.1007/s10476-024-00026-9","url":null,"abstract":"<div><p>An RD-space <span>(mathcal{X})</span> is a space of homogeneous type in the sense of Coifman and Weiss satisfying a certain reverse (volume) doubling condition.\u0000Let <span>(L)</span> be a non-negative self-adjoint operator acting on <span>(L^2(mathcal{X}))</span>.\u0000Assume that <span>(L)</span> generates an analytic semigroup <span>({mathrm{e}^{-tL}}_{t&gt;0})</span> whose kernels <span>({h_t(x,y)}_{t&gt;0})</span> satisfy a generalized Gaussian heat kernel upper estimate.\u0000Roughly speaking, the heat kernel behavior is a mixture of locally Gaussian and sub-Gaussian at infinity.\u0000With the help of this Gaussian heat kernel, we first introduce a novel Morrey space and then prove that it coincides with the classical Morrey space.\u0000As applications, some new characterizations of square Morrey space are established via a Carleson measure condition.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"597 - 623"},"PeriodicalIF":0.6,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528955","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
Boundedness of some convolution-type operators on metric measure spaces 公度量空间上某些卷积型算子的有界性
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-13 DOI: 10.1007/s10476-024-00030-z
J. M. Aldaz
{"title":"Boundedness of some convolution-type operators on metric measure spaces","authors":"J. M. Aldaz","doi":"10.1007/s10476-024-00030-z","DOIUrl":"10.1007/s10476-024-00030-z","url":null,"abstract":"<div><p>We explore boundedness properties of some natural operators of\u0000convolution type in the context of metric measure spaces. Their study is suggested by certain transformations used in computer vision.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"335 - 344"},"PeriodicalIF":0.6,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00030-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504667","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
Dowker’s ergodic theorem by the Chacon–Ornstein theorem 通过查孔-奥恩斯坦定理的道克尔遍历定理
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-05 DOI: 10.1007/s10476-024-00032-x
M. Lin
{"title":"Dowker’s ergodic theorem by the Chacon–Ornstein theorem","authors":"M. Lin","doi":"10.1007/s10476-024-00032-x","DOIUrl":"10.1007/s10476-024-00032-x","url":null,"abstract":"<div><p>We deduce Dowker’s general ratio ergodic theorem, and a vari-\u0000ant of it, from the Chacon–Ornstein theorem.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"625 - 628"},"PeriodicalIF":0.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253359","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
Asymptotically uniform functions: a single hypothesis which solves two old problems 渐近均匀函数：一个假设解决两个老问题
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-05 DOI: 10.1007/s10476-024-00024-x
J.-P. Gabriel, J.-P. Berrut
{"title":"Asymptotically uniform functions: a single hypothesis which solves two old problems","authors":"J.-P. Gabriel,&nbsp;J.-P. Berrut","doi":"10.1007/s10476-024-00024-x","DOIUrl":"10.1007/s10476-024-00024-x","url":null,"abstract":"<div><p>The asymptotic study of a time-dependent function ƒ as the solution of a differential equation often leads to the question of whether its derivative <span>(f')</span> vanishes at infinity. We show that a necessary and sufficient condition for this is that <span>(f')</span> is what may be called asymptotically uniform. We generalize the result to higher order derivatives. We also show that the same property for ƒ itself is also necessary and sufficient for its one-sided improper integrals to exist. The article provides a broad study of such asymptotically uniform functions.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"481 - 492"},"PeriodicalIF":0.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00024-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253379","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
A crystalline measure that is not a Fourier quasicrystal 不属于傅立叶准晶体的晶体量
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-03 DOI: 10.1007/s10476-024-00031-y
S. Yu. Favorov
{"title":"A crystalline measure that is not a Fourier quasicrystal","authors":"S. Yu. Favorov","doi":"10.1007/s10476-024-00031-y","DOIUrl":"10.1007/s10476-024-00031-y","url":null,"abstract":"<div><p>We construct a crystalline measure on the real line that is not a\u0000Fourier quasicrystal.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"455 - 462"},"PeriodicalIF":0.6,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00031-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253100","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
A universal formula for derivation operators and applications 推导算子的通用公式及其应用
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-03 DOI: 10.1007/s10476-024-00028-7
J. Suárez de la Fuente
{"title":"A universal formula for derivation operators and applications","authors":"J. Suárez de la Fuente","doi":"10.1007/s10476-024-00028-7","DOIUrl":"10.1007/s10476-024-00028-7","url":null,"abstract":"<div><p>We give a universal formula describing derivation operators on a \u0000Hilbert space for a large class of interpolation methods. It is based on a simple new technique on \u0000“critical points” where all the derivations attain the maximum. We deduce from this a version of Kalton uniqueness theorem for such methods, in \u0000particular, for the real method. As an application of our ideas is the construction of a weak Hilbert space induced by the real <i>J</i>-method. Previously, \u0000such space was only known arising from the complex method. To complete the picture, we show, using a breakthrough of Johnson and Szankowski, nontrivial \u0000derivations whose values on the critical points grow to infinity as slowly as we wish.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"643 - 666"},"PeriodicalIF":0.6,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00028-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253201","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
On the p-Dunford–Pettis relatively compact property of Banach spaces 论巴拿赫空间的 p-Dunford-Pettis 相对紧凑特性
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-29 DOI: 10.1007/s10476-024-00027-8
I. Ghenciu
{"title":"On the p-Dunford–Pettis relatively compact property of Banach spaces","authors":"I. Ghenciu","doi":"10.1007/s10476-024-00027-8","DOIUrl":"10.1007/s10476-024-00027-8","url":null,"abstract":"<div><p>The <i>p</i>-Dunford–Pettis relatively compact property (<span>(1le p&lt;infty)</span>)\u0000is studied in individual Banach spaces and in spaces of operators. The question\u0000of whether a space of operators has the <i>p</i>-Dunford–Pettis relatively compact\u0000property is studied using Dunford–Pettis <i>p</i>-convergent evaluation operators.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"515 - 535"},"PeriodicalIF":0.6,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197201","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 weak-type iterated Hardy–Copson inequalities 加权弱型迭代哈代-科普森不等式
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-28 DOI: 10.1007/s10476-024-00021-0
V. García García, P. Ortega Salvador
{"title":"Weighted weak-type iterated Hardy–Copson inequalities","authors":"V. García García,&nbsp;P. Ortega Salvador","doi":"10.1007/s10476-024-00021-0","DOIUrl":"10.1007/s10476-024-00021-0","url":null,"abstract":"<div><p>We characterize the good weights for some weighted weak-type iterated Hardy-Copson inequalities to hold.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"493 - 513"},"PeriodicalIF":0.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00021-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172524","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
Integral operators and Carleson measures for Möbius invariant Besov spaces 莫比乌斯不变贝索夫空间的积分算子和卡列松量
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-28 DOI: 10.1007/s10476-024-00029-6
W. Yang, C. Yuan
{"title":"Integral operators and Carleson measures for Möbius invariant Besov spaces","authors":"W. Yang,&nbsp;C. Yuan","doi":"10.1007/s10476-024-00029-6","DOIUrl":"10.1007/s10476-024-00029-6","url":null,"abstract":"<div><p>We investigate an integral operator <span>(T_{t,lambda})</span> which preserves\u0000the Carleson measure for the Möbius invariant Besov space <span>(B_p)</span> on the unit ball of <span>(mathbb{C}^{n})</span>. A holomorphic function space <span>(W_beta^p)</span>, associated with the Carleson measure for <span>(B_p)</span>, is introduced. As applications for the operator <span>(T_{t,lambda})</span>, we estimate the distance from Bloch-type functions to the space <span>(W_beta^p)</span>, which extends Jones' formula. Moreover, the bounded small Hankel operators on <span>(B_p)</span> and the atomic decomposition of <span>(W_beta^p)</span> are characterized.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"683 - 716"},"PeriodicalIF":0.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172548","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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