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Composition Operators in Grand Lebesgue Spaces Grand Lebesgue空间中的复合算子
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-02-08 DOI: 10.1007/s10476-023-0201-y
A. Karapetyants, M. Lanza de Cristoforis
{"title":"Composition Operators in Grand Lebesgue Spaces","authors":"A. Karapetyants,&nbsp;M. Lanza de Cristoforis","doi":"10.1007/s10476-023-0201-y","DOIUrl":"10.1007/s10476-023-0201-y","url":null,"abstract":"<div><p>Let Ω be an open subset of ℝ<sup><i>n</i></sup> of finite measure. Let <i>f</i> be a Borel measurable function from ℝ to ℝ. We prove necessary and sufficient conditions on <i>f</i> in order that the composite function <i>T</i><sub><i>f</i></sub>[<i>g</i>] = <i>f</i> o <i>g</i> belongs to the Grand Lebesgue space <i>L</i><sub><i>p</i>),<i>θ</i></sub>(Ω) whenever <i>g</i> belongs to <i>L</i><sub><i>p</i>),<i>θ</i></sub>(Ω).</p><p>We also study continuity, uniform continuity, Hölder and Lipschitz continuity of the composition operator <i>T</i><sub><i>f</i></sub>[·] in <i>L</i><sub><i>p</i>),<i>θ</i></sub>(Ω).</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45743373","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
Arbitrarily Sparse Spectra for Self-Affine Spectral Measures 自仿射谱测度的任意稀疏谱
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-02-08 DOI: 10.1007/s10476-023-0191-9
L.-X. An, C.-K. Lai
{"title":"Arbitrarily Sparse Spectra for Self-Affine Spectral Measures","authors":"L.-X. An,&nbsp;C.-K. Lai","doi":"10.1007/s10476-023-0191-9","DOIUrl":"10.1007/s10476-023-0191-9","url":null,"abstract":"<div><p>Given an expansive matrix <i>R</i> ∈ <i>M</i><sub><i>d</i></sub>(ℤ) and a finite set of digit <i>B</i> taken from ℤ<sup><i>d</i></sup>/<i>R</i>(<i>ℤ</i><sup><i>d</i></sup>). It was shown previously that if we can find an <i>L</i> such that (<i>R, B, L</i>) forms a Hadamard triple, then the associated fractal self-affine measure generated by (<i>R, B</i>) admits an exponential orthonormal basis of certain frequency set Λ, and hence it is termed as a spectral measure. In this paper, we show that if #<i>B</i> &lt; ∣det(<i>R</i>)∣, not only it is spectral, we can also construct arbitrarily sparse spectrum Λ in the sense that its Beurling dimension is zero.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43506983","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: 7
Off-Diagonal Two Weight Bumps for Fractional Sparse Operators 分数阶稀疏算子的非对角线两个权凸
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-02-08 DOI: 10.1007/s10476-023-0204-8
R. Rahm
{"title":"Off-Diagonal Two Weight Bumps for Fractional Sparse Operators","authors":"R. Rahm","doi":"10.1007/s10476-023-0204-8","DOIUrl":"10.1007/s10476-023-0204-8","url":null,"abstract":"<div><p>In this paper, we continue some recent work on two weight boundedness of sparse operators to the “off-diagonal” setting. We use the new “entropy bumps” introduced in by Treil and Volberg and improved by Lacey and Spencer [11] and the “direct comparison bumps” introduced by Rahm and Spencer [23] and improved by Lerner [14]. Our results are “sharp” in the sense that they are sharp in various particular cases. A feature is that given the current machinery and advances, the proofs are almost trivial.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42492320","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: 1
The Growth of Meromorphic Solutions of a Class of Delay-Differential Equations 一类时滞微分方程亚纯解的增长性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-02-08 DOI: 10.1007/s10476-023-0203-9
Z. Li, J. Zhang
{"title":"The Growth of Meromorphic Solutions of a Class of Delay-Differential Equations","authors":"Z. Li,&nbsp;J. Zhang","doi":"10.1007/s10476-023-0203-9","DOIUrl":"10.1007/s10476-023-0203-9","url":null,"abstract":"<div><p>We obtain necessary conditions for certain type of rational delay-differential equations to allow the existence of a non-rational meromorphic solution with hyper-order less than one. In addition, we give a further discussion of the coefficients of a delay-differential equation with fixed degree.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42626441","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
Complex Linear Differential Equations with Solutions in Dirichlet–Morrey Spaces Dirichlet-Morrey空间中具有解的复线性微分方程
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-02-08 DOI: 10.1007/s10476-023-0205-7
Y. Sun, B. Liu, J. L. Liu
{"title":"Complex Linear Differential Equations with Solutions in Dirichlet–Morrey Spaces","authors":"Y. Sun,&nbsp;B. Liu,&nbsp;J. L. Liu","doi":"10.1007/s10476-023-0205-7","DOIUrl":"10.1007/s10476-023-0205-7","url":null,"abstract":"<div><p>The <i>n</i>th derivative criterion for functions belonging to the Dirichlet–Morrey space <span>({cal D}_p^lambda )</span> is given in this paper. Furthermore, two sufficient conditions for coefficients of the complex linear differential equation </p><div><div><span>$${f^{left( n right)}} + {A_{n - 1}}left( z right){f^{left( {n - 1} right)}} + cdots + {A_1}left( z right){f^prime } + {A_0}left( z right)f = {A_n}left( z right)$$</span></div></div><p> are obtained such that all solutions belong to <span>({cal D}_p^lambda )</span>, where <i>A</i><sub><i>j</i></sub>(<i>z</i>) are analytic functions in the unit disc, <i>j</i> = 0,…,<i>n</i>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45680630","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
Asymptotics of Sums of Sine Series with Fractional Monotonicity Coefficients 分数单调系数正弦级数和的渐近性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-01-23 DOI: 10.1007/s10476-023-0186-6
M. I. Dyachenko, A. P. Solodov
{"title":"Asymptotics of Sums of Sine Series with Fractional Monotonicity Coefficients","authors":"M. I. Dyachenko,&nbsp;A. P. Solodov","doi":"10.1007/s10476-023-0186-6","DOIUrl":"10.1007/s10476-023-0186-6","url":null,"abstract":"<div><p>We study the following question: which monotonicity order implies upper and lower estimates of the sum of a sine series <span>(gleft( {{boldsymbol{b}},x} right) = sumnolimits_{k = 1}^infty {{b_k}} )</span> sin <i>kx</i> near zero in terms of the function <span>(vleft( {{boldsymbol{b}},x} right) = xsumnolimits_{k = 1}^{left[ {pi /x} right]} {k{b_k}} )</span>. Our results complete, on a qualitative level, the studies began by R. Salem and continued by S. Izumi, S. A. Telyakovskiĭ and A. Yu. Popov.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50507539","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: 1
A Derivative-Free Characterization of the Weighted Besov Spaces 加权Besov空间的一个无导数刻画
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-01-23 DOI: 10.1007/s10476-023-0187-5
W. Pan, H. Wulan
{"title":"A Derivative-Free Characterization of the Weighted Besov Spaces","authors":"W. Pan,&nbsp;H. Wulan","doi":"10.1007/s10476-023-0187-5","DOIUrl":"10.1007/s10476-023-0187-5","url":null,"abstract":"<div><p>We obtain a characterization of the weighted Besov space <span>({{cal B}_K}left( p right))</span> for a weight function <i>K</i>, 0 &lt; <i>p</i> &lt; ∞, in terms of symmetric and derivative-free double integrals with the weight function <i>K</i> in the unit disc. As a by-product, we give a modification of the identity of Littlewood—Paley type for the Bergman space. As an application, a derivative-free characterization of <span>({{cal Q}_K})</span> type spaces is obtained.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45698849","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 Inverse Poletsky Inequality in Metric Spaces and Prime Ends 度量空间和素数端点上的逆Poletsky不等式
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-01-23 DOI: 10.1007/s10476-023-0192-8
E. Sevost’yanov
{"title":"On the Inverse Poletsky Inequality in Metric Spaces and Prime Ends","authors":"E. Sevost’yanov","doi":"10.1007/s10476-023-0192-8","DOIUrl":"10.1007/s10476-023-0192-8","url":null,"abstract":"<div><p>We study mappings defined in the domain of a metric space that distort the modulus of families of paths by the type of the inverse Poletsky inequality. It is proved that such mappings have a continuous extension to the boundary of the domain in terms of prime ends. Under some additional conditions, the families of such mappings are equicontinuous in the closure of the domain with respect to the space of prime ends.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43185484","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: 1
New Aspects of Universality of Hurwitz Zeta-Functions Hurwitz-Zeta函数普遍性的新方面
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-01-23 DOI: 10.1007/s10476-023-0188-4
A. Laurinčikas
{"title":"New Aspects of Universality of Hurwitz Zeta-Functions","authors":"A. Laurinčikas","doi":"10.1007/s10476-023-0188-4","DOIUrl":"10.1007/s10476-023-0188-4","url":null,"abstract":"<div><p>We construct an absolutely convergent Dirichlet series connected to the classical Hurwitz zeta-function. The shifts of this function approximate analytic functions defined in the right-hand side of the critical strip.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0188-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42959134","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
The Hilbert Transform for Dunkl Differential Operators Associated to the Reflection Group ℤ2 与反射群有关的Dunkl微分算子的Hilbert变换
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-01-23 DOI: 10.1007/s10476-023-0189-3
I. A. López P
{"title":"The Hilbert Transform for Dunkl Differential Operators Associated to the Reflection Group ℤ2","authors":"I. A. López P","doi":"10.1007/s10476-023-0189-3","DOIUrl":"10.1007/s10476-023-0189-3","url":null,"abstract":"<div><p>The aim of this paper is to introduce the Dunkl—Hilbert transform <i>H</i><sup><i>k</i></sup>, with <i>k</i> ≥ 0, induced by the Dunkl differential operator and associated with the reflection group ℤ<sub>2</sub>. For this end, we establish that the Dunkl—Poisson kernel and the conjugate Dunkl—Poisson kernel satisfy the Cauchy—Riemann equations in the Dunkl context. We prove the continuity of <i>H</i><sup><i>k</i></sup> on <i>L</i><sup>p</sup>(<i>w</i><sub><i>k</i></sub>) for 1 &lt; <i>p</i> &lt; ∞, where <i>w</i><sub><i>k</i></sub>(<i>x</i>) = ∣<i>x</i>∣<sup>2<i>k</i></sup>. Finally, we introduce the maximal Hilbert operator <i>H</i><span>\u0000 <sup><i>k</i></sup><sub>*</sub>\u0000 \u0000 </span> and establish an analogue of Cotlar’s theorem.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45258882","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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