Averages of simplex Hilbert transforms
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- by Polona Durcik and Joris Roos PDF
- Proc. Amer. Math. Soc. 149 (2021), 633-647 Request permission
Abstract:
We study a multilinear singular integral obtained by taking averages of simplex Hilbert transforms. This multilinear form is also closely related to Calderón commutators and the twisted paraproduct. We prove $L^p$ bounds in dimensions two and three and give a conditional result valid in all dimensions.References
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Additional Information
- Polona Durcik
- Affiliation: Department of Mathematics, California Institute of Technology, 1200 E California Boulevard, Pasadena, California 91125
- Address at time of publication: Schmid College of Science and Technology, Chapman University, One University Drive, Orange, California 92866
- MR Author ID: 1157699
- Email: durcik@chapman.edu
- Joris Roos
- Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706
- Address at time of publication: Department of Mathematical Sciences, University of Massachusetts Lowell, Lowell, Massachusetts 01854
- MR Author ID: 1222805
- ORCID: 0000-0003-0140-6769
- Email: joris_roos@uml.edu
- Received by editor(s): December 31, 2018
- Published electronically: December 7, 2020
- Communicated by: Alexander Iosevich
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 633-647
- MSC (2010): Primary 42B20; Secondary 42B15
- DOI: https://doi.org/10.1090/proc/15196
- MathSciNet review: 4198071