ESTIMATES FOR DECREASING REARRANGEMENTS OF CONVOLUTION AND COVERINGS OF CONES

Abstract In the paper, we obtain lower estimates for decreasing rearrangements of the convolutions through decreasing rearrangements of kernels and functions to be convolved. These estimates show the exactness of some corollaries of O’Neil’s upper estimates for convolutions. The results are applied for equivalent descriptions of the cones of decreasing rearrangements for generalized Bessel and Riesz potentials. These are the key results for study of integral properties of potentials.