Approximation by trigonometric polynomials in weighted Morrey spaces
TBILISI MATHEMATICAL JOURNAL, cilt.13, sa.1, ss.123-138, 2020 (ESCI)
- 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).