Maximal multilinear Calderón-Zygmund operators with non-doubling measures

Abstract

Under the assumption that μ is a non-doubling measure on R d which only satises some growth condition, the authors prove that the maximal multilinear CalderónZygmund operator is bounded from L p 1 (μ) × · · · × L pm (μ) into L p (μ) for any p1, . . . , pm ∈ (1, ∞) and p with 1/p = 1/p1 + · · · + 1/pm, and bounded from L p 1 (μ) × · · · × L pm (μ) into weak-L p (μ) if there exists any p i = 1.Furthermore, the authors establish a weighted weak-type estimate for the maximal multilinear CalderónZygmund operator.

Sharp weighted estimates for multi-linear Calderón-Zygmund operators on non-homogeneous spaces

“…An alternate proof the above result is available in [16] for R d with polynomial growth measures. However our approach is more classical in nature.…”

The Hardy Space H1 with Non-doubling Measures and Their Applications

“…See [150] for the boundedness of commutators generated by multilinear singular integrals and RBMO . / functions of Tolsa, and [85] for the boundedness of the maximal multilinear Calderón-Zygmund operators. • Let .X ; d; / be a metric measure space with satisfying the polynomial growth condition.…”