On fractional operators with more than one singularity

Abstract

. Let 0 ≤ α < n , m ∈ N and let T α,m be an integral operator given by a kernel of the form K ( x,y ) = k 1 ( x − A 1 y ) k 2 ( x − A 2 y ) ...k m ( x − A m y ) , where A i are invertible matrices and each k i satisfies a fractional size and a generalized fractional H¨ormander condition that depends on α . In this survey, written in honour to Eleonor Harboure, we collect several results about boundedness in different spaces of the operator T α,m , obtained along the last 35 years by several members of the Analysis Group of FAMAF, UNC.