Holomorphic Campanato Spaces on the Unit Ball

TL;DR

This paper investigates the properties of holomorphic Campanato spaces on the unit ball in complex space, focusing on Carleson measures and oscillation behaviors of Hardy functions in a non-isotropic setting.

Contribution

It provides a Carleson measure characterization of holomorphic Campanato spaces on the unit ball, extending understanding of oscillation and regularity in several complex variables.

Findings

Characterization of holomorphic Campanato spaces via Carleson measures

Analysis of oscillation properties of Hardy functions in non-isotropic metrics

Extension of classical results to higher-dimensional complex spaces

Abstract

As outlined below, this paper is devoted to a Carleson-type-measure-based study of the holomorphic Campanato $2$-space on the open unit ball $\mathbb B_n$ of $\mathbb C^n$, comprising all Hardy $2$-functions whose oscillations in non-isotropic metric balls on the compact unit sphere $\mathbb S_n$ are proportional to some power of the radius other than the dimension $n\ge 1$.