Let1≤p≤+∞be a real number andMbe the centered Hardy–Littlewood maximaloperator. Then, there exists a non-constant functionf∈Lp(Rn)such thatM(f)=f,if and only ifn≥3andn/(n−2)
Referencias bibliográficas
B. Borjaski and P. Hajlasz, Pointwise inequalities for Sobolev functions and some applications, Studia Math. 106 (1993), 77–92.
J.L. Lewis, On very weak solutions of certain elliptic systems, Comm. Partial Differential Equations, 18 (1993), 1515–1537.
E.M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, N. J., 1970.
E.M. Stein and J.O. Strömberg, Behavior of maximal functions in $\mathbb{R}^n$, for large $n$, Ark. Mat. 21 (1983), 259–269.