Multilinear multipliers and singular integrals with smooth kernels on Hardy spaces

Cruz-Uribe, David, OFS; Nguyen, Hanh

doi:10.1090/tran/8007

Multilinear multipliers and singular integrals with smooth kernels on Hardy spaces
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by David Cruz-Uribe, OFS and Hanh Van Nguyen PDF

Trans. Amer. Math. Soc. 374 (2021), 3801-3825 Request permission

Abstract:

We consider weighted norm inequalities for multilinear multipliers whose symbols satisfy a product-type Hörmander condition. Our approach is to consider a more general family of multilinear singular integral operators associated to a family of smooth kernels that satisfy an $L^r$-Schwartz regularity condition. We give conditions for these operators to satisfy weighted Hardy space estimates and derive our results for multipliers as a special case. As an additional application, we use Rubio de Francia extrapolation to prove multilinear estimates on the variable exponent Hardy spaces.

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