On fractional operators with more than one singularity

Abstract

Let 0 ≤ α < n, m ∈ N and let Tα,m be an integral operator given by a kernel of the form K(x, y) = k1(x − A1y)k2(x − A2y) . . . km(x − Amy), where Ai are invertible matrices and each ki 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 Tα,m, obtained along the last 35 years by several members of the Analysis Group of FAMAF, UNC.