Integral means of holomorphic functions as generic log-convex weights

Evgueni Doubtsov

paper

Integral means of holomorphic functions as generic log-convex weights

arXiv:1706.02078

Abstract

Let $H o l (B_{d})$ denote the space of holomorphic functions on the unit ball $B_{d}$ of $C^{d}$ , $d \geq 1$ . Given a log-convex strictly positive weight $w (r)$ on $[0, 1)$ , we construct a function $f \in H o l (B_{d})$ such that the standard integral means $M_{p} (f, r)$ and $w (r)$ are equivalent for any $0 < p \leq \infty$ . Also, we obtain similar results related to volume integral means.

5 pages