{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:14:43Z","timestamp":1760058883325,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T00:00:00Z","timestamp":1746662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangzhou Huashang College Featured Research Project","award":["2024HSTS08","12471176","2021ZDJS055","HKGSXJ2022-37"],"award-info":[{"award-number":["2024HSTS08","12471176","2021ZDJS055","HKGSXJ2022-37"]}]},{"name":"NNSF of China","award":["2024HSTS08","12471176","2021ZDJS055","HKGSXJ2022-37"],"award-info":[{"award-number":["2024HSTS08","12471176","2021ZDJS055","HKGSXJ2022-37"]}]},{"name":"Key Construction Discipline Scientific Research Ability Promotion Project of Guangdong Province","award":["2024HSTS08","12471176","2021ZDJS055","HKGSXJ2022-37"],"award-info":[{"award-number":["2024HSTS08","12471176","2021ZDJS055","HKGSXJ2022-37"]}]},{"name":"Science and Technology Plan Project of Guangzhou Haizhu District","award":["2024HSTS08","12471176","2021ZDJS055","HKGSXJ2022-37"],"award-info":[{"award-number":["2024HSTS08","12471176","2021ZDJS055","HKGSXJ2022-37"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Hilbert-type inequalities derive from the classical Hilbert inequality, and their theoretical work has key applications not only in operator theory but also in various analytic disciplines. In this paper, we have achieved the parametric conditions required for the construction of such inequalities, as well as the expressions for the optimal constant factors. Through the utilization of the construction theorem for Hilbert-type multiple integral inequalities with homogeneous kernels, our investigation centers on a Hilbert-type multiple integral inequality that involves multivariable upper limit functions and higher-order partial derivatives. Furthermore, we apply these results to discuss the boundedness and operator norms of integral operators with identical kernels.<\/jats:p>","DOI":"10.3390\/axioms14050355","type":"journal-article","created":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T06:47:15Z","timestamp":1746686835000},"page":"355","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Construction Conditions and Applications of a Hilbert-Type Multiple Integral Inequality Involving Multivariable Upper Limit Functions and Higher-Order Partial Derivatives"],"prefix":"10.3390","volume":"14","author":[{"given":"Yong","family":"Hong","sequence":"first","affiliation":[{"name":"Artificial Intelligence College, Guangzhou Huashang College, Guangzhou 511300, China"}]},{"given":"Qian","family":"Zhao","sequence":"additional","affiliation":[{"name":"Artificial Intelligence College, Guangzhou Huashang College, Guangzhou 511300, China"}]},{"given":"Zhihong","family":"Zhao","sequence":"additional","affiliation":[{"name":"Graduate School, Beijing Institute of Technology, Zhuhai 519088, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,8]]},"reference":[{"key":"ref_1","unstructured":"Hardy, G.H., Littlewood, J.E., and Polya, G. 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A new Hardy-Hilbert-type integral inequality involving multiple upper limit function and one derivation function of higher order. Axioms, 12.","DOI":"10.3390\/axioms12050499"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/355\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:29:21Z","timestamp":1760030961000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/355"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,8]]},"references-count":27,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["axioms14050355"],"URL":"https:\/\/doi.org\/10.3390\/axioms14050355","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,5,8]]}}}