Multilinear Calderón–Zygmund operators on the product of Lebesgue spaces with non-doubling measures

Abstract

Under the assumption that μ is a non-doubling measure on R d , the author proves that for the multilinear Calderón–Zygmund operator, its boundedness from the product of Hardy space H 1 ( μ ) × H 1 ( μ ) into L 1 / 2 ( μ ) implies its boundedness from the product of Lebesgue spaces L p 1 ( μ ) × L p 2 ( μ ) into L p ( μ ) with 1 < p 1 , p 2 < ∞ and p satisfying 1 / p = 1 / p 1 + 1 / p 2 .