A comparison between the Bergman and Szegő kernels of the non-smooth worm domain D'_β

2015/05/09 by Alessandro Monguzzi, Monguzzi, Alessandro
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1505.02272

Abstract

In this work we provide an asymptotic expansion for the Szegő kernel associated to a suitably defined Hardy space on the the non-smooth worm domain D'_β. After describing the singularities of the kernel, we compare it with an asymptotic expansion of the Bergman kernel. In particular, we show that the Bergman kernel has the same singularities of the first derivative of the Szegő kernel with respect to any of the variables. On the side, we prove the boundedness of the Bergman projection operator on Sobolev spaces of integer order.

Related

• The Bergman kernel and projection on non-smooth worm domains
• Analysis and geometry on worm domains
• Comparison of the Bergman and Szegö kernels
• Hardy spaces and the Szegő projection of the non-smooth worm domain D'_β
• A Direct Connection Between the Bergman and Szegő Kernels