L-harmonic functions and the exponential square class (Q1106994)

It is proved for a restricted class of second order linear differential operators L if \(Lu=0\) in \({\mathbb{R}}_+^{d+1}\), \(u|_{{\mathbb{R}}\quad d}=f\) then if the Lusin area integral of u, \(Su\in L^{\infty}\), 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].