Norm estimates for Bessel-Riesz operators on generalized Morrey spaces

Abstract

We revisit the properties of Bessel-Riesz operators and present a different proof of the boundedness of these operators on generalized Morrey spaces. We also obtain an estimate for the norm of these operators on generalized Morrey spaces in terms of the norm of their kernels on an associated Morrey space. As a consequence of our results, we reprove the boundedness of fractional integral operators on generalized Morrey spaces, especially of exponent $1$, and obtain a new estimate for their norm.

Keywords

• Bessel-Riesz operator
• fractional integral operator
• generalized Morrey space