Boundedness of weighted Hadamard–Bergman and weighted variable Hadamard–Bergman convolution operators

This paper is a continuation of recent studies of the class of Hadamard–Bergman operators presented in the works of Karapetyants and Samko (Complex Anal Oper Theory 14:77, 2020). We consider a specific weighted case in which we can provide more detailed conditions for the boundedness in weighted Lebesgue spaces. As the main result, we prove boundedness theorems (sufficient conditions and also necessary conditions for positive kernels) for weighted (variable) Hadamard–Bergman operators using the technique of operators with homogeneous kernels, developed earlier in real analysis.