{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:32:27Z","timestamp":1760146347783,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T00:00:00Z","timestamp":1730160000000},"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","2021ZDJS055","HKGSXJ2022-37","2021KTSCX085"],"award-info":[{"award-number":["2024HSTS08","2021ZDJS055","HKGSXJ2022-37","2021KTSCX085"]}]},{"name":"Key Construction Discipline Scientific Research Ability Promotion Project of Guangdong Province","award":["2024HSTS08","2021ZDJS055","HKGSXJ2022-37","2021KTSCX085"],"award-info":[{"award-number":["2024HSTS08","2021ZDJS055","HKGSXJ2022-37","2021KTSCX085"]}]},{"name":"Science and Technology Plan Project of Guangzhou Haizhu District","award":["2024HSTS08","2021ZDJS055","HKGSXJ2022-37","2021KTSCX085"],"award-info":[{"award-number":["2024HSTS08","2021ZDJS055","HKGSXJ2022-37","2021KTSCX085"]}]},{"name":"Characteristic Innovation Project of Universities in Guangdong Province (Natural Science), China","award":["2024HSTS08","2021ZDJS055","HKGSXJ2022-37","2021KTSCX085"],"award-info":[{"award-number":["2024HSTS08","2021ZDJS055","HKGSXJ2022-37","2021KTSCX085"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Super-homogeneous functions including homogeneous functions, quasi-homogeneous functions, and several non-homogeneous functions are considered. Using the weight function method, the construction conditions of Hilbert-type multiple integral inequalities with super-homogeneous kernels are first discussed. Then, using the obtained results, the construction problem of bounded multiple integral operators with super-homogeneous kernels in weighted Lebesgue space is discussed, and the necessary and sufficient conditions for operator boundedness and the operator norm formula are obtained.<\/jats:p>","DOI":"10.3390\/axioms13110742","type":"journal-article","created":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T08:42:09Z","timestamp":1730191329000},"page":"742","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Necessary and Sufficient Conditions for the Boundedness of Multiple Integral Operators with Super-Homogeneous Kernels in Weighted Lebesgue Space"],"prefix":"10.3390","volume":"13","author":[{"given":"Yong","family":"Hong","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"He","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lijuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,29]]},"reference":[{"key":"ref_1","unstructured":"Hardy, G.H., Littlewood, J.E., and P\u00f3lya, G. 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Theory and Applications of Hilbert-Type Inequalities, Science Press."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/11\/742\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:23:10Z","timestamp":1760113390000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/11\/742"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,29]]},"references-count":20,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["axioms13110742"],"URL":"https:\/\/doi.org\/10.3390\/axioms13110742","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,10,29]]}}}