Sharp Hardy-Leray inequality for axisymmetric divergence-free fields

Hardy-Leray inequalities in variable Lebesgue spaces

In this paper, we prove the Hardy-Leray inequality and related inequalities in variable Lebesgue spaces. Our proof is based on a version of the Stein-Weiss inequality in variable Lebesgue spaces derived from two weight inequalities due to Melchiori and Pradolini. We also discuss an application of our results to establish an existence result for the degenerate $\pp$-Laplace operator.

无源场的Sharp Hardy-Leray不等式

Sharp Hardy-Leray inequality for solenoidal fields

本文计算了 $\mathbb{R}^N$ 上无源向量场Hardy-Leray不等式的最佳常数，在无对称性假设下推导并简化了该常数，并证明其在积分有限的函数空间内无法达到。

Anisotropic Hardy-Sobolev inequality in mixed Lorentz spaces with applications to the axisymmetric Navier-Stokes equations

In this paper, we establish several new anisotropic Hardy-Sobolev inequalities in mixed Lebesgue spaces and mixed Lorentz spaces, which covers many known corresponding results. As an application, this type of inequalities allows us to generalize some regularity criteria of the 3D axisymmetric Navier-Stokes equations.