On convolution operators in the spaces of almost periodic functions and \(L^p\) spaces
The authors consider convolution operators generated by \(L^1\) functions in \(L^p\) spaces and in the spaces of Bohr, Stepanov and Besicovich of almost periodic functions. They prove that if such an operator is invertible in one of these spaces, then it is invertible in all the spaces. Next, they also prove that convolution operators have identical norms in each of two members of the couples: \(L^p\) and \(B^p\), \(BS^p\) and \(S^p\), \(C_b\) and CAP.
spaces of Bohr, Stepanov and Besicovich of almost periodic functions
scientific article; zbMATH DE number 1501861
scientific article