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Kernel smoothing operators on thick open domains 厚开域上的核平滑算子
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-08-15 DOI: 10.1007/s10476-026-00157-1
D. Giannakis, M. J. Latifi Jebelli
{"title":"Kernel smoothing operators on thick open domains","authors":"D. Giannakis,&nbsp;M. J. Latifi Jebelli","doi":"10.1007/s10476-026-00157-1","DOIUrl":"10.1007/s10476-026-00157-1","url":null,"abstract":"<div><p>We study the convergence properties of a general family of normalized Markovian kernels on a domain <span>(Omega)</span>in the Euclidean space. Based on the notion of a thick set we show that a local Hardy-Littlewood inequality holds in <span>(L^p(Omega))</span>, <span>(p in (1, infty])</span> when <span>(Omega)</span>is thick. We then establish pointwise and <span>(L^p(Omega))</span>convergence for families of convolution operators with a Markov normalization on <span>(Omega)</span>.\u0000 We further discuss convergence properties of bistochastic kernels where the corresponding integral operators preserve constant functions and integrals.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"493 - 516"},"PeriodicalIF":0.5,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-026-00157-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782043","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
Estimations for optimal constants in Hardy-Littlewood-Sobolev inequalities on balls and annuli 球和环空上Hardy-Littlewood-Sobolev不等式中最优常数的估计
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-08-10 DOI: 10.1007/s10476-026-00169-x
Hong Huang, Yutian Lei
{"title":"Estimations for optimal constants in Hardy-Littlewood-Sobolev inequalities on balls and annuli","authors":"Hong Huang,&nbsp;Yutian Lei","doi":"10.1007/s10476-026-00169-x","DOIUrl":"10.1007/s10476-026-00169-x","url":null,"abstract":"<div><p>The Hardy-Littlewood-Sobolev inequalities are a distinguished class of functional inequalities, with applications in the theory of nonlinear PDEs and mathematical physics. Those inequalities are known in sharp form, after the work of the existence of optimisers proved by Lieb in 1983. More recently, reverse Hardy-Littlewood-Sobolev inequalities have been established by Dou and Zhu in 2015, in sharp form, together with the existence of optimisers. In this paper, we investigate analogous statements in bounded domains, more specifically, balls and annuli (for different regimes of the parameters involved in the inequalities). The estimates from above and below for the sharp constants of the inequalities are obtained. These bounds of the best constant are helpful to well understand the graviton self-energy and the Coulomb energy in the Thomas-Fermi model describing electron gas.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"517 - 531"},"PeriodicalIF":0.5,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782475","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
Rademacher's theorem for Calderón-Zygmund-type spaces Calderón-Zygmund-type空间的Rademacher定理
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-08-04 DOI: 10.1007/s10476-026-00170-4
T. Lamby
{"title":"Rademacher's theorem for Calderón-Zygmund-type spaces","authors":"T. Lamby","doi":"10.1007/s10476-026-00170-4","DOIUrl":"10.1007/s10476-026-00170-4","url":null,"abstract":"<div><p>Rademacher's Theorem can be interpreted as an almost everywhere little-o improvement principle: if a function admits a uniform pointwise first-order Lipschitz control at every point, then this control improves to a vanishing one at almost every point. In the language of Calderón-Zygmund pointwise spaces, this means that\u0000</p><div><div><span>$$f in T^infty_1(x) {rm for, all},, x in mathbb{R}^d {implies}, f in t^infty_1(x) text{for a.e.},, x in mathbb{R}^d.$$</span></div></div><p>The purpose of this paper is to establish an analogous almost everywhere improvement principle in a refined \u0000<span>(L^p)</span> setting. We consider pointwise \u0000Calderón-Zygmund spaces \u0000<span>(T^p_{phi}(x))</span> \u0000defined via polynomial approximation in \u0000<span>(L^p)</span> with a function parameter \u0000<span>(phi)</span>, allowing for fractional \u0000regularity indices and logarithmic corrections through Boyd functions. We prove that, under natural assumptions on \u0000<span>(phi)</span>, the uniform membership\u0000</p><div><div><span>$$f in T^p_{phi}(x) quad {rm for,, all},, x in E$$</span></div></div><p>\u0000on a measurable set \u0000<span>(E subset mathbb{R}^d)</span> \u0000implies an almost everywhere improvement to a vanishing approximation rate, namely\u0000</p><div><div><span>$$f in t^p_{phi,n+1}(x) quad text{for a.e. } x in E,$$</span></div></div><p>\u0000where <span>(n &lt; underline{b}(phi) leq overline{b}(phi) &lt; n+1)</span>.</p><p>The proof combines measurability arguments, a generalized Whitney extension theorem, and fine properties of Sobolev spaces. We also show \u0000that this result is essentially sharp: in general, one cannot expect almost everywhere membership in \u0000<span>(t^p_{phi,n}(x))</span> for fractional indices, and explicit counterexamples are provided.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"555 - 569"},"PeriodicalIF":0.5,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782108","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
Inequality for (L^q)-means of the derivative and (L^0)-means of polynomials with zeros outside the disk 不等式(L^q) -导数的均值和(L^0) -圆盘外有零的多项式的均值
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-08-04 DOI: 10.1007/s10476-026-00172-2
A. E. Rokina
{"title":"Inequality for (L^q)-means of the derivative and (L^0)-means of polynomials with zeros outside the disk","authors":"A. E. Rokina","doi":"10.1007/s10476-026-00172-2","DOIUrl":"10.1007/s10476-026-00172-2","url":null,"abstract":"<div><p>We study a special case of the Markov-Nikol’skii inequality for the class of algebraic polynomials with complex coefficients that do not vanish in the disc. This inequality estimates the <span>(L^q)</span>-mean of the derivative of order <span>(k)</span> of a polynomial on the interval <span>([-1,1])</span> from above by the <span>(L^0)</span>-mean (geometric mean) of the polynomial itself on the same interval. We obtain the exact constant in this inequality for <span>(qge2)</span> and arbitrary <span>(k)</span> and characterize all extremal polynomials. </p><p>Additionally, for the class of polynomials with zeros in the closed disk, we study the extremal case of Turán's inequality when the <span>(L^r)</span>-mean on <span>([-1,1] )</span> of the derivative of order <span>( k=n)</span> (the degree of the polynomial) is estimated from below by the <span>(L^q)</span>-mean of the polynomial itself on the interval. We obtain the exact constant in this inequality for all <span>(0 le r, q le infty)</span> and describe the set of extremal polynomials.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"637 - 652"},"PeriodicalIF":0.5,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782109","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
Some notes on the (L^{1})-norm of Walsh-Fejér kernels 关于walsh - fej薪金核的(L^{1}) -范数的一些注释
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-08-03 DOI: 10.1007/s10476-026-00167-z
I. Blahota
{"title":"Some notes on the (L^{1})-norm of Walsh-Fejér kernels","authors":"I. Blahota","doi":"10.1007/s10476-026-00167-z","DOIUrl":"10.1007/s10476-026-00167-z","url":null,"abstract":"<div><p>The <span>(L^1)</span>-norm of kernel functions plays a central role in studying the convergence properties of the Walsh-Fourier system. Although when viewed as a sequence, in many cases only their boundedness matters, the precise values of the individual terms can also be of interest. It is known that for all <span>(N in mathbb{N})</span>, the <span>(L^1)</span>-norms of the <span>(2^N)</span>-th and <span>((2^{N+1} - 1))</span>-th kernel functions are exactly 1. In this paper, we prove that these are the only such cases: for every other <span>(n in mathbb{P})</span>, the strict inequality <span>(|K_n|_1 &gt; 1)</span> holds. Finally, we present additional closed-form expressions for selected subsequences of <span>(|K_n|_1)</span> as illustrative \u0000 examples, using the recursive formula of Toledo [8].</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"457 - 466"},"PeriodicalIF":0.5,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782267","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 skew James type constant in Banach spaces 巴拿赫空间中的偏詹姆士型常数
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-07-29 DOI: 10.1007/s10476-026-00166-0
Z.-Y. Rao, Q. Wu, Q. Liu, Q.-C. Ni, Y.-X. Wang
{"title":"The skew James type constant in Banach spaces","authors":"Z.-Y. Rao,&nbsp;Q. Wu,&nbsp;Q. Liu,&nbsp;Q.-C. Ni,&nbsp;Y.-X. Wang","doi":"10.1007/s10476-026-00166-0","DOIUrl":"10.1007/s10476-026-00166-0","url":null,"abstract":"<div><p>Takahashi introduced the James type constant \u0000<span>(mathcal{J}_{mathcal{X}, t}(tau))</span>. Motivated by this, we define a skew James type constant <span>(mathcal{J}_{ t}[tau,mathcal{X}])</span> as a natural generalization of the classical constant. We establish its equivalent representations and fundamental properties in Banach spaces. Furthermore, we examine the relationship between the constant <span>(mathcal{J}_{ t}[tau,mathcal{X}])</span> and the modulus of convexity. Finally, we introduce a new geometric constant <span>(mathcal{G}_t(mathcal{X}))</span> \u0000and establish several of its properties.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"619 - 636"},"PeriodicalIF":0.5,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783467","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
Normal criteria for two families of meromorphic functions concerning shared functions 关于共享函数的两个亚纯函数族的正规判据
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-07-29 DOI: 10.1007/s10476-026-00174-0
Q. Yang, P. Yang, X. Pang
{"title":"Normal criteria for two families of meromorphic functions concerning shared functions","authors":"Q. Yang,&nbsp;P. Yang,&nbsp;X. Pang","doi":"10.1007/s10476-026-00174-0","DOIUrl":"10.1007/s10476-026-00174-0","url":null,"abstract":"<div><p>In this paper, we primarily investigate normality problems concerning two families of functions sharing fixed points or meromorphic functions. For the normality criterion of two families of holomorphic functions sharing fixed points, we find a new idea by constructing novel auxiliary functions and employing functional transformations, thereby resolving the normality problem at the fixed point <span>(z = 0)</span>. Furthermore, in the normality criteria for two families of meromorphic functions sharing values, we generalize the shared constants in previous results to shared meromorphic functions, thus extending existing theorems.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"697 - 708"},"PeriodicalIF":0.5,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783469","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
Isoperimetric inequality for harmonic functions 调和函数的等周不等式
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-07-29 DOI: 10.1007/s10476-026-00171-3
M. Mateljević, B. Purtić
{"title":"Isoperimetric inequality for harmonic functions","authors":"M. Mateljević,&nbsp;B. Purtić","doi":"10.1007/s10476-026-00171-3","DOIUrl":"10.1007/s10476-026-00171-3","url":null,"abstract":"<div><p>A version of the isoperimetric inequality holds for a function <span>(f)</span>\u0000for which log <span>(|f|)</span> is subharmonic. We characterize a subclass of harmonic functions\u0000which has these properties. For the class of functions <span>(h(z_1, ldots ,z_n))</span>, <span>(z_i in mathbb{U})</span>, which\u0000separately have these properties, we prove a version of isoperimetric inequality.\u0000In addition, we prove a version of Gabriel’s theorem for the subclass of harmonic\u0000functions.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"571 - 586"},"PeriodicalIF":0.5,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783470","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
Directional short-time fractional Fourier analysis of quasiasymptotic properties of distributions 分布拟渐近性质的定向短时分数傅里叶分析
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-07-29 DOI: 10.1007/s10476-026-00168-y
A. Ferizi, K. Hadzi-Velkova Saneva
{"title":"Directional short-time fractional Fourier analysis of quasiasymptotic properties of distributions","authors":"A. Ferizi,&nbsp;K. Hadzi-Velkova Saneva","doi":"10.1007/s10476-026-00168-y","DOIUrl":"10.1007/s10476-026-00168-y","url":null,"abstract":"<div><p>In this paper, we establish several Abelian- and Tauberian-type results that characterize the quasiasymptotic behavior of Schwartz tempered distributions through the asymptotic properties of their directional short-time fractional Fourier transform.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"475 - 492"},"PeriodicalIF":0.5,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783389","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 Koebe-type functions for harmonic quasiconformal mappings 关于调和拟共形映射的koebe型函数
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-07-29 DOI: 10.1007/s10476-026-00173-1
Z.-G. Wang, J.-L. Qiu, A. Rasila
{"title":"On Koebe-type functions for harmonic quasiconformal mappings","authors":"Z.-G. Wang,&nbsp;J.-L. Qiu,&nbsp;A. Rasila","doi":"10.1007/s10476-026-00173-1","DOIUrl":"10.1007/s10476-026-00173-1","url":null,"abstract":"<div><p>This paper studies a class of Koebe-type harmonic quasiconformal\u0000functions. It is motivated by the shear construction of Clunie and Sheil-Small\u0000[Ann. Acad. Sci. Fenn. Ser. A I Math., 9 (1984), 3–25] and the harmonic quasiconformal\u0000Koebe function. Equivalent univalence conditions, pre-Schwarzian and\u0000Schwarzian norms, coefficient inequalities, as well as growth and area theorems for\u0000this family of functions are established. These findings improve several previously\u0000known results.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 2","pages":"653 - 666"},"PeriodicalIF":0.5,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783468","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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