{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:45:33Z","timestamp":1760237133379,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T00:00:00Z","timestamp":1582848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"This work is supported by the National Natural Science Foundation (No. 61772140), and Science and Technology Planning Project Item of Guangzhou City (No. 201707010229).","award":["61772140;201707010229"],"award-info":[{"award-number":["61772140;201707010229"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We establish a new inequality of Hilbert-type containing positive homogeneous kernel       ( min { m , n } )  \u03bb      and derive its equivalent forms. Based on the obtained Hilbert-type inequality, we discuss its equivalent forms and give the operator expressions in some particular cases.<\/jats:p>","DOI":"10.3390\/sym12030342","type":"journal-article","created":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T07:50:53Z","timestamp":1583135453000},"page":"342","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms"],"prefix":"10.3390","volume":"12","author":[{"given":"Bicheng","family":"Yang","sequence":"first","affiliation":[{"name":"Institute of Applied Mathematics, Longyan University, Longyan 364012, Fujian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7413-6563","authenticated-orcid":false,"given":"Shanhe","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Longyan University, Longyan 364012, Fujian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aizhen","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Guangdong University of Education, Guangzhou 510303, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,28]]},"reference":[{"key":"ref_1","unstructured":"Hardy, G.H., Littlewood, J.E., and Polya, G. 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