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 $n\ge 1$.

27 pages