G. Leng

collaborators

7 papers

math.FA2026

A square-root complex inequality and its induced metric structure

Gangsong Leng, Lecheng Yang

Let $(I^c ◯, I^¼)$ be a finite measure space with $M = I^¼ (I^c ◯) > 0$ . We investigate the integral form, stability, and metric geometry associated with a square-root complex. After proving the…

math.FA2026

Distance Stability for the Integral Hardy and Carleman Inequalities

Gangsong Leng

We study stability forms of two classical integral inequalities: Hardy's integral inequality and the integral Carleman inequality, also known as the PÃ³lya--Knopp inequality. The s…

math.FA2026

Two Integral Sliding-Window Inequalities for Maximal Convolutions

Gangsong Leng, Cheng Li

We prove two sliding-window inequalities for maximal convolutions. The first concerns the multiplicative maximal convolution. If $f$ and $g$ are nonnegative continuous functions on…

math.AP2026

A Density-Distance Version of the Carlen--Frank--Lieb Stability Theorem

Gangsong Leng

Carlen, Frank and Lieb studied stability estimates for the lowest eigenvalue of a SchrÃ¶dinger operator by decomposing the problem into a stability estimate for HÃ¶lder's inequalit…

math.FA2026

An Optimal Stability Theorem for HÃ¶lder's Inequality

Gangsong Leng, Yifan Lu

We prove an optimal $L^{1}$ stability theorem for HÃ¶lder's inequality. Let $p > 1$ , $q > 1$ , and $1/ p + 1/ q = 1$ . If $a_{k}, b_{k} \geq 0$ and \[ \sum_{k=1}^n a_k=\sum_{k=1}^n b_k=1, \] then \[ 1-…

math.MG2026

A Median Version of Hardy's Inequality

Gangsong Leng

Motivated by a discrete inequality problem proposed by Duanyang Zhang as Problem 6 of the 2022 Spring NSMO, we prove a median version of Hardy's inequality. For a nonnegative funct…