Sublinear Operators in Generalized Weighted Morrey Spaces

V. Kokilashvili^a*, A. Meskhi^a**, and H. Rafeiro^b
Translated by O. Sipacheva

^a Razmadze Mathematical Institute, Javakhishvili Tbilisi State University, Tbilisi, 0177 Georgia

^bPontificia Universidad Javeriana, Bogotá, Colombia

Correspondence to: *e-mail: kokil@rmi.ge,
Correspondence to: **e-mail: meskhi@rmi.ge

Received 31 May, 2016

Abstract—Generalized weighted Morrey spaces defined on spaces of homogeneous type are introduced by using weight functions in the Muckenhoupt class. Theorems on the boundedness of a large class of sublinear operators on these spaces are presented. The classes of sublinear operators under consideration contain a whole series of important operators of harmonic analysis, such as, e.g., maximal functions, singular and fractional integrals, Bochner–Riesz means, and so on.

DOI: 10.1134/S1064562416050203