Compactification and decompactification by weights on Bergman spaces
We characterize the symbols φ for which there exists a weight w such that the weighted composition operator MwCφ is compact on the weighted Bergman space Bα2. We also characterize the symbols for which there exists a weight w such that MwCφ is bounded but not compact. We also investigate when there...
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| Published in | Journal of mathematical analysis and applications Vol. 513; no. 2; p. 126212 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
15.09.2022
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-247X 1096-0813 |
| DOI | 10.1016/j.jmaa.2022.126212 |
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| Abstract | We characterize the symbols φ for which there exists a weight w such that the weighted composition operator MwCφ is compact on the weighted Bergman space Bα2. We also characterize the symbols for which there exists a weight w such that MwCφ is bounded but not compact. We also investigate when there exists w such that MwCφ is Hilbert-Schmidt on Bα2. |
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| AbstractList | We characterize the symbols φ for which there exists a weight w such that the weighted composition operator MwCφ is compact on the weighted Bergman space Bα2. We also characterize the symbols for which there exists a weight w such that MwCφ is bounded but not compact. We also investigate when there exists w such that MwCφ is Hilbert-Schmidt on Bα2. |
| ArticleNumber | 126212 |
| Author | Rodríguez-Piazza, Luis Lefèvre, Pascal Li, Daniel Queffélec, Hervé |
| Author_xml | – sequence: 1 givenname: Pascal surname: Lefèvre fullname: Lefèvre, Pascal email: pascal.lefevre@univ-artois.fr organization: Univ. Artois, UR 2462, Laboratoire de Mathématiques de Lens (LML), F-62 300 Lens, France – sequence: 2 givenname: Daniel surname: Li fullname: Li, Daniel email: daniel.li@univ-artois.fr organization: Univ. Artois, UR 2462, Laboratoire de Mathématiques de Lens (LML), F-62 300 Lens, France – sequence: 3 givenname: Hervé orcidid: 0000-0001-9663-5470 surname: Queffélec fullname: Queffélec, Hervé email: Herve.Queffelec@univ-lille.fr organization: Univ. Lille Nord de France, USTL, Laboratoire Paul Painlevé U.M.R. CNRS 8524, F-59 655 Villeneuve d'Ascq Cedex, France – sequence: 4 givenname: Luis orcidid: 0000-0002-2298-8748 surname: Rodríguez-Piazza fullname: Rodríguez-Piazza, Luis email: piazza@us.es organization: Universidad de Sevilla, Facultad de Matemáticas, Departamento de Análisis Matemático & IMUS, Calle Tarfia s/n, 41 012 Sevilla, Spain |
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| Cites_doi | 10.1007/s13398-011-0027-5 10.1016/j.jfa.2018.01.010 10.5186/aasfm.2021.4602 10.1090/S0002-9947-2013-05922-3 10.1007/978-1-4612-0887-7 10.1007/s00020-010-1795-6 10.4153/CJM-1986-043-4 10.1112/S0024610704005605 10.1090/S0002-9939-1975-0374886-9 10.1016/j.jat.2011.12.003 10.1002/9781118165621 10.1016/j.jfa.2004.01.012 10.4171/rmi/666 10.1016/j.jfa.2020.108834 |
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| Keywords | Decompactification Weighted composition operator Compactification Weighted Bergman space Composition operator Hilbert-Schmidt operator |
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| References | Lefèvre, Li, Queffélec, Rodríguez-Piazza (br0100) 2012; 28 Li (br0140) 2011; 105 Moorhouse (br0170) 2005; 219 Rudin (br0190) 1987 Shapiro (br0200) 1993 Kahane, Katznelson (br0080) 1971; 272 Zygmund (br0210) 2002 Gallardo-Gutiérrez, Kumar, Partington (br0040) 2010; 67 Duren (br0030) 2000 Garnett, Marshall (br0060) 2008; vol. 2 Rudin (br0180) 1990 Lechner, Li, Queffélec, Rodríguez-Piazza (br0090) 2018; 274 Lefèvre, Li, Queffélec, Rodríguez-Piazza (br0110) 2013; 365 Cowen, MacCluer (br0010) 1995 Hastings (br0070) 1975; 52 MacCluer, Shapiro (br0160) 1986; 38 Lefèvre, Li, Queffélec, Rodríguez-Piazza (br0130) 2021; 280 Čučković, Zhao (br0020) 2004; 70 Li, Queffélec, Rodríguez-Piazza (br0150) 2012; 164 Garnett (br0050) 2007; vol. 236 Lefèvre, Li, Queffélec, Rodríguez-Piazza (br0120) 2021; 46 Lefèvre (10.1016/j.jmaa.2022.126212_br0130) 2021; 280 Čučković (10.1016/j.jmaa.2022.126212_br0020) 2004; 70 Shapiro (10.1016/j.jmaa.2022.126212_br0200) 1993 Garnett (10.1016/j.jmaa.2022.126212_br0050) 2007; vol. 236 Rudin (10.1016/j.jmaa.2022.126212_br0180) 1990 Lefèvre (10.1016/j.jmaa.2022.126212_br0100) 2012; 28 Li (10.1016/j.jmaa.2022.126212_br0140) 2011; 105 MacCluer (10.1016/j.jmaa.2022.126212_br0160) 1986; 38 Lefèvre (10.1016/j.jmaa.2022.126212_br0120) 2021; 46 Garnett (10.1016/j.jmaa.2022.126212_br0060) 2008; vol. 2 Moorhouse (10.1016/j.jmaa.2022.126212_br0170) 2005; 219 Rudin (10.1016/j.jmaa.2022.126212_br0190) 1987 Kahane (10.1016/j.jmaa.2022.126212_br0080) 1971; 272 Duren (10.1016/j.jmaa.2022.126212_br0030) 2000 Gallardo-Gutiérrez (10.1016/j.jmaa.2022.126212_br0040) 2010; 67 Hastings (10.1016/j.jmaa.2022.126212_br0070) 1975; 52 Lechner (10.1016/j.jmaa.2022.126212_br0090) 2018; 274 Lefèvre (10.1016/j.jmaa.2022.126212_br0110) 2013; 365 Li (10.1016/j.jmaa.2022.126212_br0150) 2012; 164 Cowen (10.1016/j.jmaa.2022.126212_br0010) 1995 Zygmund (10.1016/j.jmaa.2022.126212_br0210) 2002 |
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| SubjectTerms | Compactification Composition operator Decompactification Hilbert-Schmidt operator Weighted Bergman space Weighted composition operator |
| Title | Compactification and decompactification by weights on Bergman spaces |
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