L-harmonic functions and the exponential square class

Caroline Perkins Sweezy

Vol. 147 (1991), No. 1, 187–200

DOI: 10.2140/pjm.1991.147.187

Abstract

It is proved for a restricted class of second order linear differential operators L if Lu = 0 in R₊^d+1, u|_R^d = f then if the Lusin area integral of u, Su ∈ L^∞, f is in the exponential square class. This extends the work of Chang, Wilson and Wolff who proved the same result for harmonic u [3].

Mathematical Subject Classification 2000

Primary: 35J25

Secondary: 31B25, 42B25

Milestones

Received: 30 November 1988

Published: 1 January 1991