{"title":"Two-Sided Estimates of the Norm for a Class of Matrix Operators","authors":"A. A. Kalybay","doi":"10.1134/s1055134422010035","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For <span>\\( 1<p,q<\\infty \\)</span>, we find necessary and sufficient\nconditions for the validity of a discrete Hardy-type inequality </p><span>$$ \\left (\\sum \\limits\n_{n=1}^{\\infty }|(Af)_n|^q\\right )^{\\frac {1}{q}} \\le C\\left (\\sum \\limits\n_{k=1}^{\\infty }|f_k|^p\\right )^{\\frac {1}{p}}$$</span><p> for\na class of matrix operators of the form <span>\\((Af)_n=\\sum \\limits _{k=1}^{n}a_{n,k}f_k \\)</span>, where <span>\\(n\\ge 1 \\)</span>.\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"68 9","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134422010035","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For \( 1<p,q<\infty \), we find necessary and sufficient
conditions for the validity of a discrete Hardy-type inequality
期刊介绍:
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.