Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces

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Cakir Z., Aykol C., Guliyev V. S., ŞERBETÇİ A.

CARPATHIAN MATHEMATICAL PUBLICATIONS, vol.13, no.3, pp.750-763, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.15330/cmp.13.3.750-763
  • Journal Name: CARPATHIAN MATHEMATICAL PUBLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.750-763
  • Keywords: variable exponent weighted Morrey space, best approximation, trigonometric polynomial, direct and inverse theorem, SOBOLEV EMBEDDINGS, RIESZ-POTENTIALS, LEBESGUE SPACES, OPERATORS
  • Ankara University Affiliated: Yes

Abstract

In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces M-p(.),M-lambda(.) (I-0, w), where w is a weight function in the Muckenhoupt A(p(.)) (I-0) class. We get a characterization of K-functionals in terms of the modulus of smoothness in the spaces M-p(.),M-lambda(.) (I-0, w). Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces (M) over tilde (p(.),lambda(.)) (I-0, w), the closure of the set of all trigonometric polynomials in M-p(.),M-lambda(.) (I-0, w).