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Title: | On the Hilbert matrix norm on positively indexed weighted Bergman spaces | Authors: | Dmitrović, Dušica Karapetrović, Boban |
Affiliations: | Real and Complex Analysis Real and Complex Analysis |
Keywords: | Hilbert matrix;Operator norm;Weighted Bergman spaces | Issue Date: | 1-Oct-2023 | Rank: | M21a | Publisher: | Springer | Journal: | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas | Abstract: | The Hilbert matrix is bounded on weighted Bergman spaces Aαp if and only if 1 < α+ 2 < p with the conjectured norm π/sin(α+2)πp . In the case of positively indexed weighted Bergman spaces, that is, in the case when α> 0 , the conjecture was confirmed for α≤ p , where α is a unique zero of the function Φα(x)=2x2-(4(α+2)+1)x+2α+2x+α+2 on the interval (α+ 2 , 2 (α+ 2)) . In this note we prove, that if α> 0 , then the conjecture is valid for all 3α4+2+(3α4+2)2-α+22≤p. This improves the best previously known result for all α>12 . |
Description: | This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s13398-023-01469-9 |
URI: | https://research.matf.bg.ac.rs/handle/123456789/1395 | ISSN: | 15787303 | DOI: | 10.1007/s13398-023-01469-9 |
Appears in Collections: | Research outputs |
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