On maximizers of a convolution operator in -spaces

Abstract

Abstract The paper is concerned with convolution operators in , whose kernels are in , which act from into , where . It is shown that for there exists a maximizer (a function with -norm 1) at which the supremum of the -norm of the convolution is attained. A special analysis is carried out for the cases in which one of the exponents , , or is or . Bibliography: 12 titles.