Fundamental iterated convolution inequalities in weighted Lp spaces and their applications

Abstract

In this paper, we obtain the inequalities for the iterated convolution and their applications to physical problems. We also get the inequality ∥∥∥∥∥∥ ∑ m ⎛ ⎝ r ∏ j=1 ∗(Fm,jρm,j) ⎞ ⎠ ⎛ ⎝ r ∏ j=1 ∗|ρm,j| ⎞ ⎠ 1 p−1 ∥∥∥∥∥∥ Lp(Rn) ∑ m r ∏ j=1 ‖Fm,j‖Lp(Rn,|ρm,j|) and its applications in Lp(R, |ρ|) space. Mathematics subject classification (2000): 44A35, 35A22, 26D20.