On the atomic decomposition for Hardy spaces

James Michael Wilson

Vol. 116 (1985), No. 1, 201–207

DOI: 10.2140/pjm.1985.116.201

Abstract

We give an extremely easy proof of the atomic decomposition for distributions in H^p(R₊ⁿ⁺¹), 0 < p ≤ 1. Our proof uses only properties of the nontangential maximal function u^∗. We then adapt our argument to give a “direct” proof of the Chang-Fefferman decomposition for H^p(R₊² × R₊²).

Mathematical Subject Classification 2000

Primary: 42B30

Milestones

Received: 26 April 1983

Revised: 8 July 1983

Published: 1 January 1985