A characterization of two-weighted inequalities for maximal, singular operators andtheir commutators in generalized weighted Morrey spaces

AYKOL KOCAKUŞAKLI C., Hasanov J., Safarov Z. V.

FUNCTIONES ET APPROXIMATIO, COMMENTARII MATHEMATICI, cilt.-1, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: -1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.7169/facm/1924
  • Dergi Adı: FUNCTIONES ET APPROXIMATIO, COMMENTARII MATHEMATICI
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
  • Anahtar Kelimeler: Maximal operator, Calder?n-Zygmund singular operators, commutator, weighted Lebesgue space, generalized weighted Morrey space, BMO space, INTEGRAL-OPERATORS, ELLIPTIC-EQUATIONS, NORM INEQUALITIES, GREEN-FUNCTION, HARDY, BOUNDEDNESS, BOUNDARY
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper we give a characterization of two-weighted inequalities for maximal, singular operators and their commutators in generalized weighted Morrey spaces Mp,phi omega(Rn). We prove the boundedness of maximal operator M and maximal commutators [M, b] from the spaces Mp,phi 1 1 (Rn) to the spaces Mp,phi 2 2 (Rn), where 1 < p < oo, 0 < delta < 1 and (omega 1, omega 2) E omega delta omega delta A_p(Rn). We also prove the boundedness of the Calderon-Zygmund singular operators T and their commutators [b, T] from Mp,phi 1 1 (Rn) to Mp,phi 2 2 (Rn ). Finally we give generalized weighted omega delta omega delta Morrey a priori estimates as applications of our results.