Huoxiong Wu

A Class of Commutators for Multilinear Fractional Integrals in Nonhomogeneous Spaces

Let be a nondoubling measure on . A class of commutators associated with multilinear fractional integrals and RBMO() functions are introduced and shown to be bounded on product of Lebesgue spaces with .

A NOTE ON THE ENDPOINT REGULARITY OF THE HARDY–LITTLEWOOD MAXIMAL FUNCTIONS

In this note we give a simple proof of the endpoint regularity for the uncentred Hardy–Littlewood maximal function on

Multiple singular integrals and Marcinkiewicz integrals with mixed homogeneity along surfaces

\mathbb{R}

Compactness of Riesz transform commutator associated with Bessel operators

. Our proof is based on identities for the local maximum points of the corresponding maximal functions, which are of interest in their own right.

A note on rough singular integrals in Triebel-Lizorkin spaces and Besov spaces

This paper is devoted to studying the singular integrals and Marcinkiewicz integrals with mixed homogeneity along surfaces, which contain many classical surfaces as model examples, on the product domains Rm×Rn (m,n≥2). Under rather weak size conditions of the kernels, the Lp(Rm×Rn)-boundedness for such operators is established. These results essentially extend certain previous results.MSC:42B20, 42B25.

VECTOR-VALUED INEQUALITIES FOR THE COMMUTATORS OF SINGULAR INTEGRALS WITH ROUGH KERNELS

Let λ > 0 and

A LIPSCHITZ ESTIMATE FOR MULTILINEAR OSCILLATORY SINGULAR INTEGRALS WITH ROUGH KERNELS

{\Delta _\lambda }: = - \frac{{{d^2}}}{{d{x^2}}} - \frac{{2\lambda }}{x}\frac{d}{{dx}}

On Marcinkiewicz integral operators with rough kernels

Δλ:=−d2dx2−2λxddx be the Bessel operator on R+:= (0,∞). We first introduce and obtain an equivalent characterization of CMO(R+, x2λdx). By this equivalent characterization and by establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function b ∈ BMO(R+, x2λdx) is in CMO(R+, x2λdx) if and only if the Riesz transform commutator xxxx is compact on Lp(R+, x2λdx) for all p ∈ (1,∞).