Linear and bilinear $T(b)$ theorems à la Stein
Authors:
Árpád Bényi and Tadahiro Oh
Journal:
Proc. Amer. Math. Soc. Ser. B 2 (2015), 1-16
MSC (2010):
Primary 42B20
DOI:
https://doi.org/10.1090/bproc/18
Published electronically:
October 9, 2015
MathSciNet review:
3406428
Full-text PDF Open Access
View in AMS MathViewer
Abstract | References | Similar Articles | Additional Information
Abstract: In this work, we state and prove versions of the linear and bilinear $T(b)$ theorems involving quantitative estimates, analogous to the quantitative linear $T(1)$ theorem due to Stein.
- Árpád Bényi and Tadahiro Oh, Smoothing of commutators for a Hörmander class of bilinear pseudodifferential operators, J. Fourier Anal. Appl. 20 (2014), no. 2, 282–300. MR 3200923, DOI 10.1007/s00041-013-9312-3
- Michael Christ, Lectures on singular integral operators, CBMS Regional Conference Series in Mathematics, vol. 77, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1990. MR 1104656
- Michael Christ and Jean-Lin Journé, Polynomial growth estimates for multilinear singular integral operators, Acta Math. 159 (1987), no. 1-2, 51–80. MR 906525, DOI 10.1007/BF02392554
- Guy David and Jean-Lin Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. (2) 120 (1984), no. 2, 371–397. MR 763911, DOI 10.2307/2006946
- G. David, J.-L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), no. 4, 1–56 (French). MR 850408, DOI 10.4171/RMI/17
- C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215
- Loukas Grafakos, Modern Fourier analysis, 2nd ed., Graduate Texts in Mathematics, vol. 250, Springer, New York, 2009. MR 2463316, DOI 10.1007/978-0-387-09434-2
- Loukas Grafakos and Rodolfo H. Torres, Multilinear Calderón-Zygmund theory, Adv. Math. 165 (2002), no. 1, 124–164. MR 1880324, DOI 10.1006/aima.2001.2028
- Loukas Grafakos and Rodolfo H. Torres, On multilinear singular integrals of Calderón-Zygmund type, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000), 2002, pp. 57–91. MR 1964816, DOI 10.5565/PUBLMAT_{E}sco02_{0}4
- Yong Sheng Han, Calderón-type reproducing formula and the $Tb$ theorem, Rev. Mat. Iberoamericana 10 (1994), no. 1, 51–91. MR 1271757, DOI 10.4171/RMI/145
- Jarod Hart, A new proof of the bilinear $\rm T(1)$ Theorem, Proc. Amer. Math. Soc. 142 (2014), no. 9, 3169–3181. MR 3223373, DOI 10.1090/S0002-9939-2014-12054-5
- Jarod Hart, A bilinear T(b) theorem for singular integral operators, J. Funct. Anal. 268 (2015), no. 12, 3680–3733. MR 3341962, DOI 10.1016/j.jfa.2015.02.008
- Alan McIntosh and Yves Meyer, Algèbres d’opérateurs définis par des intégrales singulières, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 8, 395–397 (French, with English summary). MR 808636
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
Retrieve articles in Proceedings of the American Mathematical Society, Series B with MSC (2010): 42B20
Retrieve articles in all journals with MSC (2010): 42B20
Additional Information
Árpád Bényi
Affiliation:
Department of Mathematics, Western Washington University, 516 High Street, Bellingham, Washington 98225
MR Author ID:
672886
Email:
arpad.benyi@wwu.edu
Tadahiro Oh
Affiliation:
School of Mathematics, The University of Edinburgh, and The Maxwell Institute for the Mathematical Sciences, James Clerk Maxwell Building, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
MR Author ID:
782317
Email:
hiro.oh@ed.ac.uk
Keywords:
$T(b)$ theorem,
$T(1)$ theorem,
Calderón-Zygmund operator,
bilinear operator
Received by editor(s):
February 8, 2015
Published electronically:
October 9, 2015
Communicated by:
Alexander Iosevich
Article copyright:
© Copyright 2015
by the authors under
Creative Commons Attribution 3.0 License
(CC BY 3.0)
