Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces

Creative Commons License

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

CARPATHIAN MATHEMATICAL PUBLICATIONS, cilt.13, sa.3, ss.750-763, 2021 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.15330/cmp.13.3.750-763
  • Dergi Adı: CARPATHIAN MATHEMATICAL PUBLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.750-763
  • Anahtar Kelimeler: variable exponent weighted Morrey space, best approximation, trigonometric polynomial, direct and inverse theorem, SOBOLEV EMBEDDINGS, RIESZ-POTENTIALS, LEBESGUE SPACES, OPERATORS
  • Ankara Üniversitesi Adresli: Evet

Özet

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).