{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T22:14:54Z","timestamp":1769120094528,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T00:00:00Z","timestamp":1768867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12471176"],"award-info":[{"award-number":["12471176"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Key Research Platforms and Projects of Universities in Guangdong Province\u2014Special Projects in Key Fields","award":["2023ZDZX4042"],"award-info":[{"award-number":["2023ZDZX4042"]}]},{"name":"Guangdong Provincial Quality Engineering Project 2023"},{"name":"Guangdong University of Education Teaching Achievement Cultivation Project 2024"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper introduces a novel multidimensional half-discrete Hardy\u2013Hilbert-type inequality that simultaneously addresses several key extensions in the literature. The inequality incorporates a general parameterized kernel involving a scalar term and the \u03b2-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\u2013Maclaurin 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.<\/jats:p>","DOI":"10.3390\/axioms15010069","type":"journal-article","created":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T11:27:58Z","timestamp":1768908478000},"page":"69","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Novel Multidimensional Refinement of the Half-Discrete Hardy\u2013Hilbert Inequality with a Parameterized Kernel and a Partial Sum Term"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2545-0310","authenticated-orcid":false,"given":"Xianyong","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mathematics, Guangdong University of Education, Guangzhou 510303, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bicheng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Guangdong University of Education, Guangzhou 510303, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,20]]},"reference":[{"key":"ref_1","unstructured":"Hardy, G.H., Littlewood, J.E., and P\u00f3lya, G. 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