Dangyang He

collaborators

4 papers

math.AP2026

Riesz transform and its related inequalities for degenerate elliptic operators of Grushin type

Dangyang He

We study the $L^{p}$ boundedness of the Riesz transform and the reverse Riesz inequality for degenerate elliptic operators of Grushin type. We prove full-range $L^{p}$ boundedness of t…

math.CA2026

Isoperimetric Inequality for degenerate elliptic operators of Grushin type

Dangyang He

Let $n, m \geq 1$ , $I^\pm \in (0, 1)$ , and $I^^{2} \geq 0$ . For the Grushin-type operator \[ L=-\nabla_x\!\cdot\!\bigl(|x|^{2Î±}\nabla_x\bigr)+|x|^{2Î²}Î_y \qquad \text{on } \mathbb R^n\times \m…

math.AP2025

On the Riesz transform and its reverse inequality on manifolds with quadratically decaying curvature

Dangyang He

We study Riesz and reverse Riesz inequalities on manifolds whose Ricci curvature decays quadratically. First, we refine existing results on the boundedness of the Riesz transform b…

math.FA2025

Isoperimetric Inequality on Manifolds with Quadratically Decaying Curvature

Dangyang He

In this paper, we investigate the reverse improvement property of Sobolev inequalities on manifolds with quadratically decaying Ricci curvature. Specifically, we establish conditio…