On Convolution Operators in the Spaces of Almost Periodic Functions and $L^p$ Spaces

Abstract

We consider convolution operators generated by $L^1$ functions in $L^p$ spaces and various spaces of almost periodic functions. It turns out to be that if such an operator is invertible in one of these spaces, then it is invertible in all the spaces we consider. Further, we prove that any convolution has identical norms in many natural couples of function spaces.