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Improved bound for the bilinear Bochner–Riesz operator

Improved bound for the bilinear Bochner–Riesz operator We study $$L^p\times L^q\rightarrow L^r$$ L p × L q → L r bounds for the bilinear Bochner–Riesz operator $$\mathcal {B}^\alpha $$ B α , $$\alpha >0$$ α > 0 in $${\mathbb {R}}^d,$$ R d , $$d\ge 2$$ d ≥ 2 , which is defined by [Equation not available: see fulltext.]We make use of a decomposition which relates the estimates for $$\mathcal {B}^\alpha $$ B α to the square function estimates for the classical Bochner–Riesz operators. In consequence, we significantly improve the previously known bounds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Annalen Springer Journals

Improved bound for the bilinear Bochner–Riesz operator

Jeong, Eunhee; Lee, Sanghyuk; Vargas, Ana
Mathematische Annalen , Volume 372 (2) – May 30, 2018
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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5831
eISSN
1432-1807
DOI
10.1007/s00208-018-1696-6
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Mathematische Annalen – Springer Journals

Published: May 30, 2018

References

  • Sharp estimates for the Bochner–Riesz operator of negative order in $${\mathbb{R}}^2$$ R 2
    Bak, J-G
  • Reconstruction of singularities from full scattering data by new estimates of bilinear Fourier multipliers
    Barceló, JA; Faraco, D; Ruiz, A; Vargas, A
  • Almost orthogonality and a class of bounded bilinear pseudodifferential operators
    Bényi, Á; Torres, RH
  • Boundedness of bilinear multipliers whose symbols have a narrow support
    Bernicot, F; Germain, P
  • The bilinear Bochner–Riesz problem
    Bernicot, F; Grafakos, L; Song, L; Yan, L
  • Estimates for the Bochner–Riesz operator with negative index
    Börjeson, L
  • Besicovitch type maximal operators and applications to Fourier analysis
    Bourgain, J
  • Bounds on oscillatory integral operators based on multiplier estimates
    Bourgain, J; Guth, L
  • The boundedness of the maximal Bochner–Riesz operator on $$L^4{\mathbb{R}}(^2)$$ L 4 R ( 2 )
    Carbery, A
  • Radial Fourier multipliers of $${\mathbb{R}} L^p(^2)$$ R L p ( 2 )
    Carbery, A; Gasper, G; Trebels, W
  • Oscillatory integrals and a multiplier problem for the disc
    Carleson, L; Sjölin, P
  • Sharp $$L^p-L^q$$ L p - L q estimates for Bochner–Riesz operators of negative index in $$\mathbb{R}^n$$ R n , $$n\ge 3$$ n ≥ 3
    Cho, Y; Kim, Y; Lee, S; Shim, Y
  • On almost everywhere convergence of Bochner–Riesz means in higher dimensions
    Christ, M
  • On commutators of singular integrals and bilinear singular integrals
    Coifman, R; Meyer, Y
  • Multilinear singular operators with fractional rank
    Demeter, C; Pramanik, M; Thiele, C
  • On the two-dimensional bilinear Hilbert transform
    Demeter, C; Thiele, C
  • Unboundedness of the ball bilinear multiplier operator
    Diestel, G; Grafakos, L
  • Inequalities for strongly singular convolution operators
    Fefferman, C
  • The multiplier problem for the ball
    Fefferman, C
  • The Marcinkiewicz multiplier condition for bilinear operators
    Grafakos, L; Kalton, N
  • The disc as a bilinear multipler
    Grafakos, L; Li, X
  • Lp estimates on the bilinear Hilbert transform for $$2
    Lacey, M; Thiele, C
  • On Calderón’s conjecture
    Lacey, M; Thiele, C
  • Improved bounds for Bochner–Riesz and maximal Bochner–Riesz operators
    Lee, S
  • Bilinear restriction estimates for surfaces with curvatures of different signs
    Lee, S
  • Square function estimates for the Bochner-Riesz means
    Lee, S
  • Improved bounds for Stein’s square functions
    Lee, S; Rogers, KM; Seeger, A
  • Minimal smoothness conditions for bilinear Fourier multipliers
    Miyachi, A; Tomita, N
  • Oscillatory integrals and spherical harmonics
    Sogge, CD
  • A bilinear approach to cone multipliers, I : restriction estimates
    Tao, T; Vargas, A
  • A bilinear approach to the restriction and Kakeya conjectures
    Tao, T; Vargas, A; Vega, L
  • A Hörmander type multiplier theorem for multilinear operators
    Tomita, N
  • A sharp bilinear cone restriction estimate
    Wolff, T