Holomorphic Campanato Spaces on the Unit Ball

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 $n\ge 1$.