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

2017/01/08 by Congwen Liu, Antti Perälä, Liu, Congwen +3
Mathematics · #47G10 #Complex Variables (math.CV) #FOS: Mathematics #Primary 32A25 #Secondary 32A36 #math.CV #msc:32A25 #msc:32A36 #msc:47G10

paper · pdf · doi:10.48550/arxiv.1701.01988

14 pages, submitted

arxiv created 2017/01/08 · arxiv updated 2017/01/10

Abstract

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.

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