A generalization of the conjugate Hardy $H^2$ spaces

TL;DR

This paper introduces a generalized form of conjugate Hardy $H^2$ spaces, explores their properties, and establishes connections with minimal $L^2$ integrals, kernels, and monotonicity in planar regions.

Contribution

It extends the theory of conjugate Hardy $H^2$ spaces, providing new properties, relations, and applications to kernels and minimal integrals in complex analysis.

Findings

Derived properties of the minimal norm in the generalized spaces.

Established monotonicity of conjugate Hardy $H^2$ kernels.

Connected conjugate Hardy kernels with Bergman kernels on planar regions.

Abstract

In this article, we consider a generalization of the conjugate Hardy $H^2$ spaces, and give some properties of the minimal norm of the generalization and some relations between the norm of the generalization and the minimal $L^2$ integrals. As applications, we give some monotonicity results for the conjugate Hardy $H^2$ kernels and the Bergman kernels on planar regions, and some relations between the conjugate Hardy $H^2$ kernels and the Bergman kernels on planar regions.