Weighted Hardy operators in local generalized Orlicz-Morrey spaces

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Aykol C., Azizova Z. O., Hasanov J. J.

CARPATHIAN MATHEMATICAL PUBLICATIONS, vol.13, no.2, pp.522-533, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.15330/cmp.13.2.522-533
  • Journal Name: CARPATHIAN MATHEMATICAL PUBLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.522-533
  • Keywords: weighted Hardy operator, local generalized Orlicz-Morrey space, local BMO space, MAXIMAL FUNCTIONS, INEQUALITIES
  • Ankara University Affiliated: Yes

Abstract

In this paper, we find sufficient conditions on general Young functions (phi, psi) and the functions (phi 1, phi 2) ensuring that the weighted Hardy operators A(omega)(alpha) and A(omega)(alpha) are of strong type from a local generalized Orlicz-Morrey space M-phi phi 1(0, loc), (R-n) into another local generalized Orlicz-Morrey space M-Psi,M- (0, loc)(phi 2), (R-n). We also obtain the boundedness of the commutators of A(omega)(alpha) and A(omega)(alpha) from M-phi, phi 1(0, loc) (R-n) to M-psi, phi 2(0, loc)(R-n).