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.References
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Additional Information
- David Cruz-Uribe, OFS
- Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487
- Email: dcruzuribe@ua.edu
- Hanh Van Nguyen
- Affiliation: Department of Mathematics, University of Education, Hue University, Vietnam
- Email: nguyenvanhanh@dhsphue.edu.vn
- Received by editor(s): June 2, 2018
- Received by editor(s) in revised form: November 17, 2018, and September 14, 2019
- Published electronically: March 8, 2021
- Additional Notes: The first author was supported by research funds from the Dean of the College of Arts & Sciences, the University of Alabama. As this paper was being written he was supported by NSF Grant DMS-1362425.
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 3801-3825
- MSC (2020): Primary 42B15, 42B20, 42B30, 42B35
- DOI: https://doi.org/10.1090/tran/8007
- MathSciNet review: 4251213