Boundedness of hardy-littlewood maximal operator in the framework of lizorkin-triebel spaces

Abstract

We describe a class O of nonlinear operators which are bounded on the Lizorkin–Triebel spaces Fs p,q(Rn), for 0 < s < 1 and 1 < p, q < 1. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on Fs p,q(Rn), for 0 < s < 1 and 1 < p, q < 1 ; this extends the result of Kinnunen [9], valid for the Sobolev space H1 p (Rn).