Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 28, pp. 1-18.

Title: Discrete Stein-Weiss inequalities

Authors: Chunhong Li (Guangxi Science and Technology Normal Univ., Guangxi, China)
         Tiantian Zhou (Nanjing Normal Univ., Nanjing, China)
  
Abstract:
This article concerns the discrete Stein-Weiss inequalities with finite 
terms and with infinite terms. Such inequalities can be used to study the 
discrete Coulomb energy, nonlinear problems appearing the crystal 
lattice theory and graphs in neural  networks.
We give the limit relations between their best  constants and between 
their extremal sequences.
In addition, we obtained analogous conclusions for the reversed discrete 
Stein-Weiss inequality.

Submitted September 9, 2024. Published March 14, 2025.
Math Subject Classifications: 26D15, 40B05.
Key Words: Discrete Stein-Weiss inequality; best constant; reversed discrete Stein-Weiss inequality; extremal sequence