Xiaxing Cai

collaborators

4 papers

math.MG2026

Affine Logarithmic HLS and Beckner-Type Logarithmic Sobolev Inequalities

Xiaxing Cai

In this paper, we consider two limiting cases ( $I^\pm \to n$ and $I^\pm \to 0$ ) of the recent affine HLS inequalities by Haddad and Ludwig. As $I^\pm \to n$ , the affin…

math.MG2026

Chord Sobolev inequalities

Fernanda M. BaÃªta, Xiaxing Cai

The paper establishes a new family of sharp analytic inequalities. Together with the fractional Sobolev inequalities of Almgren and Lieb, they form a complete class of analytic ine…

math.MG2026

Affine chord Sobolev inequalities and radial mean bodies for functions

Fernanda M. BaÃªta, Xiaxing Cai

Affine isoperimetric inequalities for the functional radial mean bodies are derived from the new affine chord Sobolev inequalities, which extend the recent affine isoperimetric ine…

math.MG2025

Anisotropic fractional area measures

Xiaxing Cai

The anisotropic $s$ -fractional area measures are introduced as the first variation of the anisotropic fractional $s$ -perimeter $P_{s} (K, L)$ , with $L$ an origin symmetric convex body…