Hypersingular Marcinkiewicz Integrals along Surface with Variable Kernels on Sobolev Space and Hardy-Sobolev Space

Boundedness on Hardy-Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels

Sharp Hardy-littlewood-sobolev Inequality on the Upper Half Space

There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent λ = n−α (that is for the case of α > n). In this paper we confirm the possibility for the extension along the first direction by establishing the sharp Hardy-Littlewood-Sobolev inequ...

On Hardy-sobolev Embedding

1. Interpolation inequalities. A classical problem in analysis is to understand how “smoothness” controls norms that measure the “size” of functions. Maz’ya recognized in his classic text on Sobolev spaces the intrinsic importance of inequalities that would refine both Hardy’s inequality and Sobolev embedding. Dilation invariance and group symmetry play an essential role in determining sharp co...

Multiplicity Results for Equations with Subcritical Hardy-sobolev Exponent and Singularities on a Half-space

We prove some multiplicity results for a class of singular quasilinear elliptic problems involving the critical Hardy-Sobolev exponent and singularities on a half-space.

Critical Hardy–Sobolev Inequalities

Abstract We consider Hardy inequalities in IRn, n ≥ 3, with best constant that involve either distance to the boundary or distance to a surface of co-dimension k < n, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm. Résumé Nous étudions des inegalités de Hardy dans IRn, n ≥ 3,...