Approximation by trigonometric polynomials in weighted Morrey spaces

Cakir Z., Aykol C., Soylemez D., Serbetci A.

TBILISI MATHEMATICAL JOURNAL, vol.13, no.1, pp.123-138, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2020
  • Journal Name: TBILISI MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.123-138
  • Keywords: weighted Morrey space, Muckenhoupt class, best approximation, trigonometric polynomials, Bernstein inequality, NORM INEQUALITIES
  • Ankara University Affiliated: Yes

Abstract

In this paper we investigate the best approximation by trigonometric polynomials in weighted Morrey spaces M-p,M-lambda(I-0, w), where the weight function w is in the Muckenhoupt class A(p)(I-0) with 1 < p < infinity and I-0 = [0, 2 pi]. 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 C-infinity(I-0) in M-p,M-lambda(I-0, w). We give the characterization of K-functionals in terms of the modulus of smoothness and obtain the Bernstein type inequality for trigonometric polynomials in the spaces M-p,M-lambda(I-0, w).