Scholarlink

<p>In the paper, we give direct and inverse approximation theorems for functions defined on semiaxis and Mellin translation in appropriate <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> type space. The direct result is weaker than Jackson’s inequality, while inverse ones have a sharpened Timan-Zygmund forms. As a corollary, we obtain several equivalence statements generalizing Titchmarsh equivalence theorem. Some conditions of weighted integrability of Mellin transform are discussed and their sharpness is proved under some restrictions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Approximation theorems and integrability problems in Mellin analysis

  • 期刊论文

  • 发表日期：

    2026年4月29日

查看全文
  • Nadezhda Sergeeva,
  • Sergey Volosivets

摘要

In the paper, we give direct and inverse approximation theorems for functions defined on semiaxis and Mellin translation in appropriate \(L^2\) L 2 type space. The direct result is weaker than Jackson’s inequality, while inverse ones have a sharpened Timan-Zygmund forms. As a corollary, we obtain several equivalence statements generalizing Titchmarsh equivalence theorem. Some conditions of weighted integrability of Mellin transform are discussed and their sharpness is proved under some restrictions.