{"title":"有径向权重的伯格曼空间的科伦布伦原理","authors":"Iason Efraimidis, Adrián Llinares, Dragan Vukotić","doi":"10.1007/s40315-024-00543-6","DOIUrl":null,"url":null,"abstract":"<p>We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces <span>\\(A^p_w\\)</span> with arbitrary (non-negative and integrable) radial weights <i>w</i> in the case <span>\\(1\\le p<\\infty \\)</span>. We also notice that in every weighted Bergman space the supremum of all radii for which the principle holds is strictly smaller than one. Under the mild additional assumption <span>\\(\\liminf _{r\\rightarrow 0^+} w(r)>0\\)</span>, we show that the principle fails whenever <span>\\(0<p<1\\)</span>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Korenblum’s Principle for Bergman Spaces with Radial Weights\",\"authors\":\"Iason Efraimidis, Adrián Llinares, Dragan Vukotić\",\"doi\":\"10.1007/s40315-024-00543-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces <span>\\\\(A^p_w\\\\)</span> with arbitrary (non-negative and integrable) radial weights <i>w</i> in the case <span>\\\\(1\\\\le p<\\\\infty \\\\)</span>. We also notice that in every weighted Bergman space the supremum of all radii for which the principle holds is strictly smaller than one. Under the mild additional assumption <span>\\\\(\\\\liminf _{r\\\\rightarrow 0^+} w(r)>0\\\\)</span>, we show that the principle fails whenever <span>\\\\(0<p<1\\\\)</span>.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40315-024-00543-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40315-024-00543-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Korenblum’s Principle for Bergman Spaces with Radial Weights
We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces \(A^p_w\) with arbitrary (non-negative and integrable) radial weights w in the case \(1\le p<\infty \). We also notice that in every weighted Bergman space the supremum of all radii for which the principle holds is strictly smaller than one. Under the mild additional assumption \(\liminf _{r\rightarrow 0^+} w(r)>0\), we show that the principle fails whenever \(0<p<1\).