Norm of a multilinear integral operator from product of weighted-type spaces to weighted-type space

Abstract

We investigate the following multilinear integral operator (Formula presented.) where (Formula presented.) and (Formula presented.) is a continuous kernel function satisfying the condition (Formula presented.) for some functions (Formula presented.), which are continuous, increasing, (Formula presented.), and a function (Formula presented.), from a product of weighted-type spaces to weighted-type spaces of real functions. We calculate the norm of the operator, extending and complementing some results in the literature. We also give an explanation for a relation between integrals of an Lp integrable function and its radialization on (Formula presented.).