Spaces of DLp type and a convolution product associated with the spherical mean operator

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.