Convolution Integral Operators in Variable Bounded Variation Spaces

Commutators of integral operators with variable kernels on Hardy spaces

Abstract. Let TΩ,α (0 ≤ α < n) be the singular and fractional integrals with variable kernel Ω(x,z), and [b,TΩ,α ] be the commutator generated by TΩ,α and a Lipschitz function b. In this paper, the authors study the boundedness of [b,TΩ,α ] on the Hardy spaces, under some assumptions such as the Lr-Dini condition. Similar results and the weak type estimates at the end-point cases are also given...

Equations and Integral Operators of Convolution Type on a Bounded Interval

The purpose of this work is to introduce a study of generalized inverses for operators that characterize the equations of the form

Product - Convolution Operators and Mlxed - Norm Spaces

Conditions for boundedness and compactness of product-convolution operators g —» PhCß = h ■ (/» g) on spaces L^G) are studied. It is necessary for boundedness to define a class of "mixed-norm" spaces L,p>q){G) interpolating the Lp(G) spaces in a natural way (L^^ = Z^,). It is then natural to study the operators acting between L(/1?)(G) spaces, where G has a compact invariant neighborhood. The t...

Multilinear Singular Integral Operators with Variable Coefficients

Some recent results for bilinear or multilinear singular integrals operators are presented. The focus is on some of the results that can be viewed as natural counterparts of classical theorems in Calderón-Zygmund theory, adding to the already existing extensive literature in the subject. In particular, two different classes of operators that can be seen as bilinear counterparts of linear Calder...

A Note on Calderón-zygmund Singular Integral Convolution Operators