{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:39:14Z","timestamp":1753886354466,"version":"3.41.2"},"reference-count":8,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2008,2,26]],"date-time":"2008-02-26T00:00:00Z","timestamp":1203984000000},"content-version":"vor","delay-in-days":56,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["07C520","06C657"],"award-info":[{"award-number":["07C520","06C657"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["07C520","06C657"],"award-info":[{"award-number":["07C520","06C657"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>It is shown that some new extensions of Hilbert\u2032s integral inequality with parameter <jats:italic>\u03bb<\/jats:italic>(<jats:italic>\u03bb<\/jats:italic> &gt; 1\/2) can be established by introducing a proper weight function. In particular, when <jats:italic>\u03bb<\/jats:italic> = 1, a refinement of Hilbert\u2032s integral inequality is obtained. As applications, some new extensions of Widder\u2032s inequality and Hardy\u2010Littlewood\u2032s inequality are given.<\/jats:p>","DOI":"10.1155\/2008\/297508","type":"journal-article","created":{"date-parts":[[2008,2,28]],"date-time":"2008-02-28T14:09:52Z","timestamp":1204207792000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On New Extensions of Hilbert\u2032s Integral Inequality"],"prefix":"10.1155","volume":"2008","author":[{"given":"He","family":"Leping","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gao","family":"Mingzhe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhou","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2008,2,26]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1999.6373"},{"key":"e_1_2_5_2_2","first-page":"227","article-title":"A survey of various refinements and generalizations of Hilbert\u2032s inequalities","volume":"25","author":"Gao M.","year":"2005","journal-title":"Journal of Mathematical Research & Exposition"},{"volume-title":"Table of Integrals, Series, and Products","year":"2000","author":"Gradshteyn I. 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