Extrapolation on Lp,∞(μ)

We solve the extrapolation problem concerning bounded operators on Lp,∞(μ); that is, we give end-point estimates for sublinear operators T such that T:Lp,∞(μ)→Lp,∞(ν) is bounded with constant less than or equal to 1/(p−1)m. Applications to the Hardy–Littlewood maximal operator, the Hilbert transform and composition of operators are also given.