IUMJ

Title: Spectra of integration operators and weighted square functions

Authors: Jose Angel Pelaez and Alexandru Aleman

Issue: Volume 61 (2012), Issue 2, 775-793

Abstract:

Motivated by the study of the spectrum of integration operators
\[
T_gf(z) = \int_0^zf(\xi)g'(\xi)\mathrm{d}\xi,
\]
acting on the Hardy spaces $H^p$, we prove weighted versions of the classical estimates due to Fefferman-Stein and Littlewood-Paley which express the $H^p$-norm of an analytic function with help of its derivative.