Giordano Bruno, Alexander Pankov
On Convolution Operators in the Spaces of Almost Periodic Functions and $L^p$ Spaces

MSC:

47G10 Integral operators, See also {45P05}

Abstract: We consider operators of convolution generated by $L^1$ functions
in $L^p$ 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 functional spaces.
Keywords: convolution operators, almost periodic functions