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
M. Dziri
, M. Jelassi
and L.T. Rachdi
Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis, Tunis 1060, Tunisia
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.