A Novel Multidimensional Refinement of the Half-Discrete Hardy–Hilbert Inequality with a Parameterized Kernel and a Partial Sum Term
Year: 2026
Type: article
Abstract: This paper introduces a novel multidimensional half-discrete Hardy–Hilbert-type inequality that simultaneously addresses several key extensions in the literature. The inequality incorporates a general parameterized kernel involving a scalar term and the β-norm of a vector, and replaces the traditional discrete coefficient with a partial sum. Under suitable parameter conditions, the resulting inequality is sharper and preserves the optimal constant factor. The proof employs a systematic combination of weight-function techniques, parameter introduction, real-analysis methods, and the Euler–Maclaurin summation formula. Equivalent characterizations of the best possible constant are provided, and several meaningful corollaries are deduced, thereby unifying and generalizing a series of earlier inequalities.
Source: Axioms
Authors: Xianyong Huang, Bicheng Yang
Institution: Guangdong University of Education
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Award: G7496552270
OpenAlex ID: W7124949879