A survey on fractional operators with more than one singularity

MARÍA SILVINA RIVEROS; VIDAL, RAÚL E.

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahia Blanca; Año: 2023

0041-6932

Let 0 ≤ α < n, m ∈ N and let Tα,m be an integral operator given by a kernel of the formK(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 generalized fractional Hormander condition. In this survey written in honour to Eleonor Harboure, we collect several results about boundedness in different spaces of the operator Tα,m, obtained a long the last 35 years by several members of the Analysis Group of FAMAF, UNC.