BOUNDEDNESS OF SUBLINEAR OPERATORS GENERATED BY CALDERON-ZYGMUND OPERATORS ON GENERALIZED WEIGHTED MORREY SPACES

Karaman T., GULİYEV V. S., ŞERBETÇİ A.

ANALELE STIINTIFICE ALE UNIVERSITATII AL I CUZA DIN IASI-SERIE NOUA-MATEMATICA, vol.60, no.1, pp.227-244, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.2478/aicu-2013-0009
  • Journal Name: ANALELE STIINTIFICE ALE UNIVERSITATII AL I CUZA DIN IASI-SERIE NOUA-MATEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.227-244
  • Keywords: generalized weighted Morrey spaces, sublinear operators, Calderon-Zygmund operators, pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator, Bochner-Riesz operator, MAXIMAL OPERATOR, SUFFICIENT CONDITIONS
  • Ankara University Affiliated: Yes

Abstract

In this paper we study the boundedness for a large class of sublinear operators T generated by Calderon-Zygmund operators on generalized weighted Morrey spaces M-p,M-phi(w) with the weight function w(x) belonging to Muckenhoupt's class A(p). We find the sufficient conditions on the pair (phi(1), phi(2)) which ensures the boundedness of the operator T from one generalized weighted Morrey space M-p,(phi 1) (w) to another M-p,M-phi 2 (w) for p > 1 and from M-1,M-phi 1 (w) to the weak space WM1,phi 2 (w). In all cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on (phi(1), phi(2)), which do not assume any assumption on monotonicity of phi(1), phi(2) in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.