Hardy spaces and Szegő projection on quotient domains

2023/10/18 by Chen, Liwei, Yuan, Yuan
#32A07 #42B20 #42B30 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Primary: 32A25 #Secondary: 32A35

paper · doi:10.48550/arxiv.2310.12151

Abstract

The Hardy spaces are defined on the quotient domain of a bounded complete Reinhardt domain by a finite subgroup of U(n). The Szegő projection on the quotient domain can be studied by lifting to the covering space. This setting builds on the solution of a boundary value problem for holomorphic functions. In particular, when the covering space is either the polydisc or the unit ball in ℂⁿ, the boundary value problem can be solved. Applying this theory in ℂ², we further obtain sharp results on the L^p regularity of the Szegő projection on the symmetrized bidisc, generalized Thullen domains, and the minimal ball.

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