Commutators of certain fractional type operators with Hörmander conditions, one-weighted and two-weighted inequalities

G. IBAÑEZ FIRKORN, M.S. RIVEROS

MATHEMATICAL INEQUALITIES & APPLICATIONS

ELEMENT

Lugar: Zagreb; Año: 2020

1331-4343

In this paper we study commutators of a certain classof fractional type integral operators. These operators are given bykernels of the formK(x,y)=k_1(x-A_1y)k_2(x-A_2y)dots k_m(x-A_my),where A_i are invertible matrices and each k_i satisfies afractional size condition and generalized fractional Hörmandercondition. We obtain weighted Coifman estimates and weightedL^p(w^p) - L^q(w^q) estimates. We also give a two-weightedstrong type estimate for pairs of weights of the form (u,Su) where$u$ is an arbitrary non-negative function and S is a maximaloperator depending on the smoothness of the kernel K. For thesingular case we also give a two-weighted endpoint estimate.