Authors: | Stević, Stevo |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | On some isometries on the Bergman-Privalov class on the unit ball |
Journal: | Nonlinear Analysis, Theory, Methods and Applications |
Volume: | 75 |
Issue: | 4 |
First page: | 2448 |
Last page: | 2454 |
Issue Date: | 1-Mar-2012 |
Rank: | M21 |
ISSN: | 0362-546X |
DOI: | 10.1016/j.na.2011.10.042 |
Abstract: | Bergman-Privalov class A Nα(B) consists of all holomorphic functions on the unit ball B⊂ Cn such that ||f||A Nα:=∫ Bln(1+|f(z)|)d Vα(z) <∞, where α>-1, d Vα(z)=cα, n(1-|z| 2)αdV(z) (dV(z) is the normalized Lebesgue volume measure on B and cα, n is the normalization constant, that is, Vα(B)=1). Under a mild condition, we characterize surjective isometries (not necessarily linear) on A Nα(B), ... |
Keywords: | Bergman-Privalov class | Multiplicative isometry | Nonlinear isometry |
Publisher: | Elsevier |
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