International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 3, Pages 357-381
doi:10.1155/IJMMS.2005.357
Spaces of DLp type and a convolution product associated with the spherical mean operator
Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis, Tunis 1060, Tunisia
Received 2 June 2004; Revised 23 November 2004
Copyright © 2005 M. Dziri et al. 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 define and study the spaces ℳp(ℝ×ℝn), 1≤p≤∞, that are of DLp type. Using the harmonic analysis associated with the spherical mean operator, we give a new characterization of the dual space ℳ′p(ℝ×ℝn) and describe its bounded subsets. Next, we define a convolution product in ℳ′p(ℝ×ℝn)×Mr(ℝ×ℝn), 1≤r≤p<∞, and prove some new results.