Advertisement

Boundedness of the Maximal, Potential and Singular Operators in the Generalized Morrey Spaces

Open Access
Research Article

Abstract

We consider generalized Morrey spaces Open image in new window with a general function Open image in new window defining the Morrey-type norm. We find the conditions on the pair Open image in new window which ensures the boundedness of the maximal operator and Calderón-Zygmund singular integral operators from one generalized Morrey space Open image in new window to another Open image in new window , Open image in new window , and from the space Open image in new window to the weak space Open image in new window . We also prove a Sobolev-Adams type Open image in new window -theorem for the potential operators Open image in new window . In all the cases the conditions for the boundedness are given it termsof Zygmund-type integral inequalities on Open image in new window , which do not assume any assumption on monotonicity of Open image in new window in Open image in new window . As applications, we establish the boundedness of some Schrödinger type operators on generalized Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class. As an another application, we prove the boundedness of various operators on generalized Morrey spaces which are estimated by Riesz potentials.

Keywords

Full Article Morrey Space Publisher Note Singular Operator Generalize Morrey Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Publisher note

To access the full article, please see PDF.

Copyright information

© Vagif S. Guliyev. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of MathematicsAhi Evran UniversityKirsehirTurkey
  2. 2.Institute of Mathematics and MechanicsBakuAzerbaijan

Personalised recommendations