Weighted Bloch spaces and quadratic integrals

Abstract

Let ${\mathcal{B}}^{\omega }(B_d)$ denote the $\omega$-weighted Bloch space in the unit ball $B_d$ of ${\mathbb{C}}^d$, $d\ge 1$. We show that the quadratic integral $${\int }_x^1\frac{{\omega }^2(t)}{t}dt,0<x<1,$$ governs the radial divergence and integral reverse estimates in ${\mathcal{B}}^{\omega }(B_d)$.

9 pages