Two-sided norm estimates for Bergman-type projections with an asymptotically sharp lower bound

• Congwen Liu ^[1] ; Antti Perälä ^[2] ; Lifang Zhou ^[3]
  1. [1] University of Science and Technology of China

     University of Science and Technology of China

     China

     
  2. [2] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
  3. [3] Huzhou University

     Huzhou University

     China

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 4, 2018, págs. 1427-1441
• Idioma: inglés
• DOI: 10.4171/RMI/1031
• Texto completo no disponible (Saber más ...)
• Resumen

  • We obtain new two-sided norm estimates for the family of Bergman-type projections arising from the standard weights (1−|z|2)α where α>−1. As α→−1, the lower bound is sharp in the sense that it asymptotically agrees with the norm of the Riesz projection. The upper bound is estimated in terms of the maximal Bergman projection, whose exact operator norm we calculate. The results provide evidence towards a conjecture that was posed very recently by the first author.