Scholarlink

<p>Analogues of classical approximation theorems are established in weighted rearrangement invariant spaces for generalized moduli of smoothness of natural orders defined by one-sided Steklov means. Also, some estimates of approximation by Riesz–Zygmund and Euler means are given. As a consequence, the equivalence of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_908_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(K\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>K</mi> </math></EquationSource> </InlineEquation>-functional and two types of realization functionals defined with help of above cited means is proved. Finally, the generalized modulus of smoothness is estimated by norms of derivatives of partial Fourier sums, Riesz–Zygmund and Euler means.</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

Growth of norms of trigonometric polynomials and approximation in weighted rearrangement-invariant spaces

  • 期刊论文

  • 发表日期：

    2025年4月11日

查看全文
  • S. S. Volosivets

摘要

Analogues of classical approximation theorems are established in weighted rearrangement invariant spaces for generalized moduli of smoothness of natural orders defined by one-sided Steklov means. Also, some estimates of approximation by Riesz–Zygmund and Euler means are given. As a consequence, the equivalence of \(K\) K -functional and two types of realization functionals defined with help of above cited means is proved. Finally, the generalized modulus of smoothness is estimated by norms of derivatives of partial Fourier sums, Riesz–Zygmund and Euler means.