Approximation by trigonometric polynomials in weighted Morrey spaces

Çakır Z., Aykol C., Söylemez Özden D., Şerbetçi A.

TBILISI MATHEMATICAL JOURNAL, cilt.13, sa.1, ss.123-138, 2020 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2020
  • Dergi Adı: TBILISI MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.123-138
  • Anahtar Kelimeler: weighted Morrey space, Muckenhoupt class, best approximation, trigonometric polynomials, Bernstein inequality, NORM INEQUALITIES
  • Ankara Üniversitesi Adresli: Evet

Özet

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).