Counting functions and majorization for Jensen measures

Charles Stuart Stanton

Vol. 125 (1986), No. 2, 459–468

DOI: 10.2140/pjm.1986.125.459

Abstract

We establish a generalization for uniform algebras of the classical identities of Hardy and Stein. We use this and an estimate based on the isoperimetric inequality to give a proof of H. Alexander’s spectral area theorem. We use similar methods to prove a theorem of Axler and Shapiro about VMOA of the unit ball in Cⁿ.

Mathematical Subject Classification 2000

Primary: 32A22

Secondary: 31C05, 32A35, 32A40, 32E25, 46J10

Milestones

Received: 6 June 1985

Published: 1 December 1986