Access the full text.
Sign up today, get DeepDyve free for 14 days.
L. Grafakos (2010)
Classical Fourier Analysis
Jong-Guk Bak (1997)
SHARP ESTIMATES FOR THE BOCHNER-RIESZ OPERATOR OF NEGATIVE ORDER IN R
S Lee (2004)
Improved bounds for Bochner–Riesz and maximal Bochner–Riesz operatorsDuck Math. J., 122
Geoff Diestel, L. Grafakos (2007)
Unboundedness of the Ball Bilinear Multiplier OperatorNagoya Mathematical Journal, 185
Loukas Grafakos, Xiaochun Li (2006)
The disc as a bilinear multiplierAmerican Journal of Mathematics, 128
C. Demeter, C. Thiele (2008)
On the two-dimensional bilinear Hilbert transformAmerican Journal of Mathematics, 132
T. Tao (2003)
Some Recent Progress on the Restriction ConjecturearXiv: Classical Analysis and ODEs
T. Tao, A. Vargas (2000)
A bilinear approach to cone multipliers I. Restriction estimatesGeometric & Functional Analysis GAFA, 10
M Lacey, C Thiele (1997)
Lp estimates on the bilinear Hilbert transform for $$2
Ann. Math. (2), 146
T. Tao, A. Vargas (2000)
A bilinear approach to cone multipliers II. ApplicationsGeometric & Functional Analysis GAFA, 10
J. Cooper (1973)
SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONSBulletin of The London Mathematical Society, 5
Michael Christ (1985)
On almost everywhere convergence of Bochner-Riesz means in higher dimensions, 95
E. Stein (1993)
Harmonic Analysis (PMS-43), Volume 43: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43)
Lennart Börjeson (1986)
Estimates for the Bochner-Riesz operator with negative index.Indiana University Mathematics Journal, 35
C. Sogge (1986)
Oscillatory integrals and spherical harmonicsDuke Mathematical Journal, 53
A. Carbery, G. Gasper, W. Trebels (1984)
Radial Fourier multipliers of L(R).Proceedings of the National Academy of Sciences of the United States of America, 81 10
Sanghyuk Lee (2017)
Square function estimates for the Bochner-Riesz meansarXiv: Classical Analysis and ODEs
A. Córdoba (1982)
Geometric Fourier analysisAnnales de l'Institut Fourier, 32
M. Lacey, C. Thiele (1997)
$L^p$ estimates on the bilinear Hilbert transform for $2 < p < \infty$Annals of Mathematics, 146
M. Lacey, C. Thiele (1999)
On Calder\'on's conjecturearXiv: Classical Analysis and ODEs
and as an in
F Bernicot, P Germain (2013)
Boundedness of bilinear multipliers whose symbols have a narrow supportJ. Anal. Math., 119
F. Bernicot, P. Germain (2011)
Boundedness of bilinear multipliers whose symbols have a narrow supportJournal d'Analyse Mathématique, 119
J. Bourgain (1991)
Besicovitch type maximal operators and applications to fourier analysisGeometric & Functional Analysis GAFA, 1
L. Carleson, P. Sjölin (1972)
Oscillatory integrals and multiplier problem for the discStudia Mathematica, 44
Naohito Tomita (2010)
A Hörmander type multiplier theorem for multilinear operatorsJournal of Functional Analysis, 259
Loukas Grafakos, N. Kalton (2000)
The Marcinkiewicz multiplier condition for bilinear operatorsStudia Mathematica, 146
Jong-Guk Bak (1997)
Sharp estimates for the Bochner-Riesz operator of negative order in $\mathbf{R}^2$, 125
T. Tao (2006)
Nonlinear dispersive equations : local and global analysis, 106
Sanghyuk Lee, K. Rogers, A. Seeger (2010)
Improved bounds for Stein's square functionsProceedings of the London Mathematical Society, 104
E. Stein, Timothy Murphy (1993)
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
J. Barceló, D. Faraco, A. Ruiz, A. Vargas (2010)
Reconstruction of singularities from full scattering data by new estimates of bilinear Fourier multipliersMathematische Annalen, 346
T. Tao, A. Vargas, L. Vega (1998)
A bilinear approach to the restriction and Kakeya conjecturesJournal of the American Mathematical Society, 11
F. Bernicot, Loukas Grafakos, Liang Song, Lixin Yan (2012)
The bilinear Bochner-Riesz problemJournal d'Analyse Mathématique, 127
Sanghyuk Lee (2004)
Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operatorsDuke Mathematical Journal, 122
R. Coifman, Y. Meyer (1975)
On commutators of singular integrals and bilinear singular integralsTransactions of the American Mathematical Society, 212
A. Carbery (1983)
The boundedness of the maximal Bochner-Riesz operator on $L^4(\mathbf{R}^2)$Duke Mathematical Journal, 50
E. Stein (1971)
Singular Integrals and Di?erentiability Properties of Functions
T. Wolff (2001)
A Sharp Bilinear Cone Restriction EstimateAnnals of Mathematics, 153
A Carbery (1983)
The boundedness of the maximal Bochner–Riesz operator on $$L^4{\mathbb{R}}(^2)$$ L 4 R ( 2 )Duke Math. J., 50
C. Demeter, M. Pramanik, C. Thiele (2009)
Multilinear singular operators with fractional rankarXiv: Classical Analysis and ODEs
Sanghyuk Lee (2005)
Bilinear restriction estimates for surfaces with curvatures of different signsTransactions of the American Mathematical Society, 358
J. Bourgain, L. Guth (2010)
Bounds on Oscillatory Integral Operators Based on Multilinear EstimatesGeometric and Functional Analysis, 21
A. Córdoba (1979)
A note on Bochner-Riesz operatorsDuke Mathematical Journal, 46
Sanghyuk Lee, Ihyeok Seo (2011)
Sharp bounds for multiplier operators of negative indices associated with degenerate curvesMathematische Zeitschrift, 267
Á. Bényi, R. Torres (2004)
Almost orthogonality and a class of bounded bilinear pseudodifferential operatorsMathematical Research Letters, 11
C. Fefferman (1971)
The Multiplier Problem for the BallAnnals of Mathematics, 94
Y Cho, Y Kim, S Lee, Y Shim (2005)
Sharp $$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$$ n ≥ 3J. Funct. Anal., 218
M. Lacey, C. Thiele (1999)
On Calderon s conjectureAnnals of Mathematics, 149
Sanghyuk Lee (2003)
Some Sharp Bounds for the Cone Multiplier of Negative Order in R3Bulletin of the London Mathematical Society, 35
F Bernicot, L Grafakos, L Song, L Yan (2015)
The bilinear Bochner–Riesz problemJ. Anal. Math., 127
C. Fefferman (1970)
Inequalities for strongly singular convolution operatorsActa Mathematica, 124
Akihiko Miyachi, Naohito Tomita (2013)
Minimal smoothness conditions for bilinear Fourier multipliersRevista Matematica Iberoamericana, 29
C. Sogge (1993)
Fourier Integrals in Classical Analysis
We study $$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.
Mathematische Annalen – Springer Journals
Published: May 30, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.