A generalization of the conjugate Hardy

Abstract

In this article, we consider a generalization of the conjugate Hardy

spaces and give some properties of the minimal norm of the generalization and some relations between the norm of the generalization and the minimal

L 2 $L^2$ upper L squared

integrals. As applications, we give some monotonicity results for the conjugate Hardy

H 2 $H^2$ upper H squared

kernels and the Bergman kernels on planar regions, and some relations between the conjugate Hardy

H 2 $H^2$ upper H squared

kernels and the Bergman kernels on planar regions.