Shan Zhen Lu

The Besov Space B0,11 on Domains

Abstract Let Ω be a bounded Lipschitz domain. Define B0,11,r (Ω) = {f∈L1 (Ω): there is an F∈B0,11 (ℝn) such that F|Ω = f} and B0,11z (Ω) = {f∈B0,11 (ℝn) : f = 0 on ℝn

Weighted Boundedness for a Class of Rough Multilinear Operators

{overline Ω}

Sharp bounds for m-linear Hardy and Hilbert Operators

}. In this paper, the authors establish the atomic decompositions of these spaces. As by-products, the authors obtained the regularity on these spaces of the solutions to the Dirichlet problem and the Neumann problem of the Laplace equation of ℝn+.