Journal of the Mathematical Society of Japan

A proof of Saitoh's conjecture for conjugate Hardy $H^{2}$ kernels

Qi'an GUAN

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In this article, we obtain a strict inequality between the conjugate Hardy $H^{2}$ kernels and the Bergman kernels on planar regular regions with $n > 1$ boundary components, which is a conjecture of Saitoh.


The author was supported by NSFC-11825101, NSFC-11522101 and NSFC-11431013.

Article information

J. Math. Soc. Japan, Volume 71, Number 4 (2019), 1173-1179.

Received: 31 May 2018
First available in Project Euclid: 17 July 2019

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Zentralblatt MATH identifier

Primary: 30H10: Hardy spaces
Secondary: 30H20: Bergman spaces, Fock spaces 31C12: Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14] 30E20: Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx]

Bergman kernel conjugate Hardy $H^{2}$ kernel analytic Hardy class


GUAN, Qi'an. A proof of Saitoh's conjecture for conjugate Hardy $H^{2}$ kernels. J. Math. Soc. Japan 71 (2019), no. 4, 1173--1179. doi:10.2969/jmsj/80668066.

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