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Journal of Function Spaces and Applications
Volume 2012, Article ID 543475, 20 pages
http://dx.doi.org/10.1155/2012/543475
Research Article

Parabolic Fractional Maximal Operator in Modified Parabolic Morrey Spaces

1Department of Mathematics, Ahi Evran University, Kirsehir, Turkey
2Institute of Mathematics and Mechanics, Baku State University, Baku, Azerbaijan
3Baku State University, 1148 Baku, Azerbaijan

Received 30 August 2012; Revised 30 September 2012; Accepted 1 October 2012

Academic Editor: Dachun Yang

Copyright © 2012 Vagif S. Guliyev and Kamala R. Rahimova. 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.

Abstract

We prove that the parabolic fractional maximal operator , , is bounded from the modified parabolic Morrey space to the weak modified parabolic Morrey space if and only if and from to if and only if . Here is the homogeneous dimension on . In the limiting case we prove that the operator is bounded from to . As an application, we prove the boundedness of from the parabolic Besov-modified Morrey spaces to . As other applications, we establish the boundedness of some Schrödinger-ype operators on modified parabolic Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.