Abstract and Applied Analysis
Volume 2011 (2011), Article ID 901084, 12 pages
http://dx.doi.org/10.1155/2011/901084
Research Article

𝐻 -Distributions: An Extension of 𝐻 -Measures to an 𝐿 𝑝 - 𝐿 𝑞 Setting

Nenad Antonić1 and Darko Mitrović2

1Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička c. 30, 10 000 Zagreb, Croatia
2Faculty of Mathematics, University of Montenegro, Cetinjski put bb, 81 000 Podgorica, Montenegro

Received 13 March 2011; Revised 22 May 2011; Accepted 20 June 2011

Academic Editor: P. J. Y. Wong

Copyright © 2011 Nenad Antonić and Darko Mitrović. 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 use the continuity of Fourier multiplier operators on 𝐿 𝑝 to introduce the 𝐻 -distributions—an extension of 𝐻 -measures in the 𝐿 𝑝 framework. We apply the 𝐻 -distributions to obtain an 𝐿 𝑝 version of the localisation principle and reprove the Murat 𝐿 𝑝 - 𝐿 𝑝 ′ variant of div-curl lemma.