Improved bound for the bilinear Bochner–Riesz operator

Eunhee Jeong; Sanghyuk Lee; Ana Vargas

doi:10.1007/s00208-018-1696-6

Improved bound for the bilinear Bochner–Riesz operator

Eunhee Jeong^*
, Sanghyuk Lee
, Ana Vargas

^*Corresponding author for this work

Department of Mathematics Education

Seoul National University
Universidad Autónoma de Madrid

Research output: Contribution to journal › Journal article › peer-review

16 Scopus citations

Abstract

We study L^p× L^q→ L^r bounds for the bilinear Bochner–Riesz operator B^α, α> 0 in R^d, d≥ 2 , which is defined by [Equation not available: see fulltext.]We make use of a decomposition which relates the estimates for B^α to the square function estimates for the classical Bochner–Riesz operators. In consequence, we significantly improve the previously known bounds.

Original language	English
Pages (from-to)	581-609
Number of pages	29
Journal	Mathematische Annalen
Volume	372
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-018-1696-6
State	Published - 2018.10.1

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title = "Improved bound for the bilinear Bochner–Riesz operator",

abstract = "We study Lp× Lq→ Lr bounds for the bilinear Bochner–Riesz operator Bα, α> 0 in Rd, d≥ 2 , which is defined by [Equation not available: see fulltext.]We make use of a decomposition which relates the estimates for Bα to the square function estimates for the classical Bochner–Riesz operators. In consequence, we significantly improve the previously known bounds.",

author = "Eunhee Jeong and Sanghyuk Lee and Ana Vargas",

note = "Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Jeong, Eunhee

AU - Lee, Sanghyuk

AU - Vargas, Ana

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We study Lp× Lq→ Lr bounds for the bilinear Bochner–Riesz operator Bα, α> 0 in Rd, d≥ 2 , which is defined by [Equation not available: see fulltext.]We make use of a decomposition which relates the estimates for Bα to the square function estimates for the classical Bochner–Riesz operators. In consequence, we significantly improve the previously known bounds.

AB - We study Lp× Lq→ Lr bounds for the bilinear Bochner–Riesz operator Bα, α> 0 in Rd, d≥ 2 , which is defined by [Equation not available: see fulltext.]We make use of a decomposition which relates the estimates for Bα to the square function estimates for the classical Bochner–Riesz operators. In consequence, we significantly improve the previously known bounds.

UR - https://www.scopus.com/pages/publications/85047810144

U2 - 10.1007/s00208-018-1696-6

DO - 10.1007/s00208-018-1696-6

M3 - Journal article

AN - SCOPUS:85047810144

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VL - 372

SP - 581

EP - 609

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1-2

ER -

Improved bound for the bilinear Bochner–Riesz operator

Abstract

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