Maximal multilinear Calderón-Zygmund operators with non-doubling measures

Abstract

Under the assumption that µ is a non-doubling measure on ℝd which only satisfies some growth condition, the authors prove that the maximal multilinear Calderon-Zygmund operator is bounded from \( L^{p_1 } \) (µ) × … × \( L^{p_m } \) (µ) into Lp(µ) for any p1, … pm ∈ (1, ∞) and p with 1/p = 1/p1 + … + 1/pm, and bounded from \( L^{p_1 } \) (µ) × … × \( L^{p_m } \) (µ) into weak-Lp (µ) if there exists any pi = 1. Furthermore, the authors establish a weighted weak-type estimate for the maximal multilinear Calderon-Zygmund operator.