On the Hausdorff-Young theorem for integral operators

A Hausdorff-young Theorem for Rearrangement-invariant Spaces

The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 ^ V ̂ 2, p~ + q= 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p~ι9 it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to ςr such that the Fourier transform is a bounded linear operator from X...

A Bilinear T(b) Theorem for Singular Integral Operators

In this work, we present a bilinear Tb theorem for singular integral operators of Calderón-Zygmund type. We prove some new accretive type Littlewood-Paley results and construct a bilinear paraproduct for a para-accretive function setting. As an application of our bilinear Tb theorem, we prove product Lebesgue space bounds for bilinear Riesz transforms defined on Lipschitz curves.

Some concavity properties for general integral operators

Let $C_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{D}$. Each function $f in C_{0}(alpha)$ maps the unit disk $mathbb{D}$ onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.

Some Results for Hausdorff Operators

In this paper, we give the sufficient conditions for the boundedness of the (fractional) Hausdorff operators on the Lebesgue spaces with power weights. In some special cases, these conditions are the same and also necessary. As an application, we obtain a better lower bound of fractional Hardy operators on the Lebesgue spaces compared with a result of the paper [25]. Mathematics subject classif...

Spectral theory, Volterra integral operators and the Sturm-Liouville theorem