We define and study the spaces ℳ p ( ℝ × ℝ n ) , 1 ≤ p ≤ ∞ , that are of D L p type. Using the harmonic analysis associated with the spherical mean operator, we give a new characterization of the dual space ℳ ′ p ( ℝ × ℝ n ) and describe its bounded subsets. Next, we define a convolution product in ℳ ′ p ( ℝ × ℝ n ) × M r ( ℝ × ℝ n ) , 1 ≤ r ≤ p < ∞ , and prove some new results.