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 firstname.lastname@example.org Sanghyuk Lee email@example.com Ana Vargas firstname.lastname@example.org Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea Department of Mathematics, Universidad Autónoma de Madrid, 28049 Madrid, Spain 123
Mathematische Annalen – Springer Journals
Published: May 30, 2018
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