Improved bound for the bilinear Bochner–Riesz operator

Improved bound for the bilinear Bochner–Riesz operator Math. Ann. Mathematische Annalen https://doi.org/10.1007/s00208-018-1696-6 Improved bound for the bilinear Bochner–Riesz operator 1 1 2 Eunhee Jeong · Sanghyuk Lee · Ana Vargas Received: 9 November 2017 / Revised: 14 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 p q r Abstract We study L × L → L bounds for the bilinear Bochner–Riesz operator α d B , α> 0in R , d ≥ 2, which is defined by α 2πix ·(ξ +η) 2 2 α B ( f, g) = e (1 −|ξ | −|η| ) f (ξ ) g(η) dξ dη. d d R ×R We make use of a decomposition which relates the estimates for B to the square function estimates for the classical Bochner–Riesz operators. In consequence, we significantly improve the previously known bounds. Communicated by Loukas Grafakos. E. Jeong supported by NRF-2015R1A4A104167 (Republic of Korea), S. Lee supported by NRF-2015R1A2A2A05000956 (Republic of Korea), and A. Vargas supported by Grants MTM2013-40945-P and MTM2016-76566-P (Ministerio de Economía y Competitividad, Spain). Eunhee Jeong moonshine10@snu.ac.kr Sanghyuk Lee shklee@snu.ac.kr Ana Vargas ana.vargas@uam.es Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea Department of Mathematics, Universidad Autónoma de Madrid, 28049 Madrid, Spain 123 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Annalen Springer Journals

Improved bound for the bilinear Bochner–Riesz operator

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5831
eISSN
1432-1807
D.O.I.
10.1007/s00208-018-1696-6
Publisher site
See Article on Publisher Site

Abstract

Math. Ann. Mathematische Annalen https://doi.org/10.1007/s00208-018-1696-6 Improved bound for the bilinear Bochner–Riesz operator 1 1 2 Eunhee Jeong · Sanghyuk Lee · Ana Vargas Received: 9 November 2017 / Revised: 14 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 p q r Abstract We study L × L → L bounds for the bilinear Bochner–Riesz operator α d B , α> 0in R , d ≥ 2, which is defined by α 2πix ·(ξ +η) 2 2 α B ( f, g) = e (1 −|ξ | −|η| ) f (ξ ) g(η) dξ dη. d d R ×R We make use of a decomposition which relates the estimates for B to the square function estimates for the classical Bochner–Riesz operators. In consequence, we significantly improve the previously known bounds. Communicated by Loukas Grafakos. E. Jeong supported by NRF-2015R1A4A104167 (Republic of Korea), S. Lee supported by NRF-2015R1A2A2A05000956 (Republic of Korea), and A. Vargas supported by Grants MTM2013-40945-P and MTM2016-76566-P (Ministerio de Economía y Competitividad, Spain). Eunhee Jeong moonshine10@snu.ac.kr Sanghyuk Lee shklee@snu.ac.kr Ana Vargas ana.vargas@uam.es Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea Department of Mathematics, Universidad Autónoma de Madrid, 28049 Madrid, Spain 123

Journal

Mathematische AnnalenSpringer Journals

Published: May 30, 2018

References

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