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Geometric Properties of Normalized Le Roy-Type Mittag-Leffler Functions 归一化Le roy型Mittag-Leffler函数的几何性质
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-12-23 DOI: 10.3103/s1068362322060061
K. Mehrez, D. Bansal
{"title":"Geometric Properties of Normalized Le Roy-Type Mittag-Leffler Functions","authors":"K. Mehrez, D. Bansal","doi":"10.3103/s1068362322060061","DOIUrl":"https://doi.org/10.3103/s1068362322060061","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The main focus of the present paper is to establish sufficient conditions for the parameters of the normalized form of the generalized Le Roy-type Mittag-Leffler function have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disc. The results are new and their usefulness is depicted by deducing several interesting corollaries. The results improve several results available in the literature for the Mittag-Leffler function.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138530352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Estimates for Riesz Transforms Associated with Schrödinger Operators 与Schrödinger算子相关的Riesz变换的一些估计
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-12-23 DOI: 10.3103/s1068362322060097
Y. H. Wang
{"title":"Some Estimates for Riesz Transforms Associated with Schrödinger Operators","authors":"Y. H. Wang","doi":"10.3103/s1068362322060097","DOIUrl":"https://doi.org/10.3103/s1068362322060097","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Let <span>(mathcal{L}=-Delta+V)</span> be the Schrödinger operator on <span>(mathbb{R}^{n},)</span> where <span>(ngeq 3,)</span> and nonnegative potential <span>(V)</span> belongs to the reverse Hölder class <span>(RH_{q})</span> with <span>(n/2leq q&lt;n.)</span> Let <span>(H^{p}_{mathcal{L}}(mathbb{R}^{n}))</span> denote the Hardy space related to <span>(mathcal{L})</span> and <span>(BMO_{mathcal{L}}(mathbb{R}^{n}))</span> denote the dual space of <span>(H^{1}_{mathcal{L}}(mathbb{R}^{n}).)</span> In this paper, we show that <span>(T_{alpha,beta}=V^{alpha}nablamathcal{L}^{-beta})</span> is bounded from <span>(H^{p_{1}}_{mathcal{L}}(mathbb{R}^{n}))</span> into <span>(L^{p_{2}}(mathbb{R}^{n}))</span> for <span>(dfrac{n}{n+delta^{prime}}&lt;p_{1}leq 1)</span> and <span>(dfrac{1}{p_{2}}=dfrac{1}{p_{1}}-dfrac{2(beta-alpha)}{n},)</span> where <span>(delta^{prime}=min{1,2-n/q_{0}})</span> and <span>(q_{0})</span> is the reverse Hölder index of <span>(V.)</span> Moreover, we prove <span>(T^{*}_{alpha,beta})</span> is bounded on <span>(BMO_{mathcal{L}}(mathbb{R}^{n}))</span> when <span>(beta-alpha=1/2.)</span>\u0000</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138530339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Problems of Convergence of General Fourier Series 一般傅里叶级数收敛性的几个问题
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-12-23 DOI: 10.3103/s1068362322060085
V. Tsagareishvili, G. Tutberidze
{"title":"Some Problems of Convergence of General Fourier Series","authors":"V. Tsagareishvili, G. Tutberidze","doi":"10.3103/s1068362322060085","DOIUrl":"https://doi.org/10.3103/s1068362322060085","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Banach [1] proved that good differential properties of function do not guarantee the a.e. convergence of the Fourier series of this function with respect to general orthonormal systems (ONS). On the other hand it is very well known that a sufficient condition for the a.e. convergence of an orthonormal series is given by the Menshov–Rademacher Theorem. The paper deals with sequence of positive numbers <span>((d_{n}))</span> such that multiplying the Fourier coefficients <span>((C_{n}(f)))</span> of functions with bounded variation by these numbers one obtains a.e. convergent series of the form <span>(sum_{n=1}^{infty}d_{n}C_{n}(f)varphi_{n}(x).)</span> It is established that the resulting conditions are best possible.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138530351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Meromorphic Functions Sharing Three Values with Their Derivatives in an Angular Domain 角域上共享三个值及其导数的亚纯函数
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-12-23 DOI: 10.3103/s1068362322060048
B. Pan, W. C. Lin
{"title":"Meromorphic Functions Sharing Three Values with Their Derivatives in an Angular Domain","authors":"B. Pan, W. C. Lin","doi":"10.3103/s1068362322060048","DOIUrl":"https://doi.org/10.3103/s1068362322060048","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we investigate the uniqueness of transcendental meromorphic functions sharing three values with their derivatives in an arbitrary small angular domain including a Borel direction. The results extend the corresponding results from Gundersen, Mues and Steinmetz, Zheng, Li et al., and Chen.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138530350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 $$L^{p}$$-Greedy Universal Functions with Respect to the Generalized Walsh System 关于广义Walsh系统的$$L^{p}$$ -贪心泛函数
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-12-01 DOI: 10.3103/s106836232206005x
S. A. Episkoposyan, T. Grigoryan, L. Simonyan
{"title":"On the $$L^{p}$$-Greedy Universal Functions with Respect to the Generalized Walsh System","authors":"S. A. Episkoposyan, T. Grigoryan, L. Simonyan","doi":"10.3103/s106836232206005x","DOIUrl":"https://doi.org/10.3103/s106836232206005x","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73582257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Product of Subsets in Periodic Groups 关于周期群中子集的积
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-12-01 DOI: 10.3103/s1068362322060036
V. S. Atabekyan, V. G. Mikaelyan
{"title":"On the Product of Subsets in Periodic Groups","authors":"V. S. Atabekyan, V. G. Mikaelyan","doi":"10.3103/s1068362322060036","DOIUrl":"https://doi.org/10.3103/s1068362322060036","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74249574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 a Riemann Boundary Value Problem in the Space of $$boldsymbol{p}$$-Summable Functions with Infinite Index $$boldsymbol{p}$$空间中的一个Riemann边值问题-无穷指标可和函数
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-12-01 DOI: 10.3103/s1068362322060024
S. Aghekyan
{"title":"On a Riemann Boundary Value Problem in the Space of $$boldsymbol{p}$$-Summable Functions with Infinite Index","authors":"S. Aghekyan","doi":"10.3103/s1068362322060024","DOIUrl":"https://doi.org/10.3103/s1068362322060024","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75960748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Estimates for Riesz Transforms Associated with Schrödinger Operators 与Schrödinger算子相关的Riesz变换的一些估计
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-11-15 DOI: 10.54503/0002-3043-2022.57.6-81-94
Y. H. Wang
{"title":"Some Estimates for Riesz Transforms Associated with Schrödinger Operators","authors":"Y. H. Wang","doi":"10.54503/0002-3043-2022.57.6-81-94","DOIUrl":"https://doi.org/10.54503/0002-3043-2022.57.6-81-94","url":null,"abstract":"Abstract Let $$mathcal{L}=-Delta+V$$ be the Schrödinger operator on $$mathbb{R}^{n},$$ where $$ngeq 3,$$ and nonnegative potential $$V$$ belongs to the reverse Hölder class $$RH_{q}$$ with $$n/2leq q<n.$$ Let $$H^{p}_{mathcal{L}}(mathbb{R}^{n})$$ denote the Hardy space related to $$mathcal{L}$$ and $$BMO_{mathcal{L}}(mathbb{R}^{n})$$ denote the dual space of $$H^{1}_{mathcal{L}}(mathbb{R}^{n}).$$ In this paper, we show that $$T_{alpha,beta}=V^{alpha}nablamathcal{L}^{-beta}$$ is bounded from $$H^{p_{1}}_{mathcal{L}}(mathbb{R}^{n})$$ into $$L^{p_{2}}(mathbb{R}^{n})$$ for $$dfrac{n}{n+delta^{prime}}<p_{1}leq 1$$ and $$dfrac{1}{p_{2}}=dfrac{1}{p_{1}}-dfrac{2(beta-alpha)}{n},$$ where $$delta^{prime}=min{1,2-n/q_{0}}$$ and $$q_{0}$$ is the reverse Hölder index of $$V.$$ Moreover, we prove $$T^{*}_{alpha,beta}$$ is bounded on $$BMO_{mathcal{L}}(mathbb{R}^{n})$$ when $$beta-alpha=1/2.$$","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82711129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Ideal Transforms Defined by an Ideal 论由理想定义的理想变换
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-11-15 DOI: 10.54503/0002-3043-2022.57.6-62-69
Y. Sadegh, J. A’zami, S. Yazdani
{"title":"On the Ideal Transforms Defined by an Ideal","authors":"Y. Sadegh, J. A’zami, S. Yazdani","doi":"10.54503/0002-3043-2022.57.6-62-69","DOIUrl":"https://doi.org/10.54503/0002-3043-2022.57.6-62-69","url":null,"abstract":"Abstract Let $$R$$ be a commutative Noetherian ring, $$I$$ an ideal of $$R$$ , and $$M$$ an $$R$$ -module. The ambiguous structure of $$I$$ -transform functor $$D_{I}(-)$$ makes the study of its properties attractive. In this paper we gather conditions under which $$D_{I}(R)$$ and $$D_{I}(M)$$ appear in certain roles. It is shown under these conditions that $$D_{I}(R)$$ is a Cohen–Macaulay ring, regular ring, $$cdots$$ and $$D_{I}(M)$$ can be regarded as a Noetherian, flat, $$cdots R$$ -module. We also present a primary decomposition of zero submodule of $$D_{I}(M)$$ and secondary representation of $$D_{I}(M)$$ .","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88566425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Volterra and Wiener–Hopf Integral Operators and Corresponding Equations of the First Kind 第一类Volterra和Wiener-Hopf积分算子及相应方程
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2022-10-01 DOI: 10.3103/S1068362322050028
L. G. Arabadzhyan
{"title":"On Volterra and Wiener–Hopf Integral Operators and Corresponding Equations of the First Kind","authors":"L. G. Arabadzhyan","doi":"10.3103/S1068362322050028","DOIUrl":"https://doi.org/10.3103/S1068362322050028","url":null,"abstract":"","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86396034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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