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Tb theorem on product spaces

Published online by Cambridge University Press:  28 March 2016

YONGSHENG HAN ,
MING-YI LEE  and
CHIN-CHENG LIN
YONGSHENG HAN
Affiliation:
Department of Mathematics, Auburn University, Auburn, Alabama 36849-5310, U.S.A. e-mail: hanyong@mail.auburn.edu
MING-YI LEE
Affiliation:
Department of Mathematics, National Central University, Chung-Li, Taiwan 320, Republic of China. e-mail: mylee@math.ncu.edu.tw, clin@math.ncu.edu.tw
CHIN-CHENG LIN
Affiliation:
Department of Mathematics, National Central University, Chung-Li, Taiwan 320, Republic of China. e-mail: mylee@math.ncu.edu.tw, clin@math.ncu.edu.tw
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Abstract

In this paper, we prove a Tb theorem on product spaces $\mathbb{R}$n × $\mathbb{R}$m, where b(x1, x2) = b1(x1)b2(x2), b1 and b2 are para-accretive functions on $\mathbb{R}$n and $\mathbb{R}$m, respectively.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 1 , July 2016 , pp. 117 - 141
Copyright
Copyright © Cambridge Philosophical Society 2016 

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References

REFERENCES

[1]David, G. and Journé, J.-L.. A boundedness criterion for generalised Calderón–Zygmund operators. Ann. of Math. 120 (1984), 371–397.CrossRefGoogle Scholar
[2]David, G., Journé, J.-L. and Semmes, S.. Operateurs de Calderón–Zygmund, fonctions para-accretive et interpolation. Rev. Mat. Iberoamericana 1 (1985), no. 4, 1–56.Google Scholar
[3]Frazier, M. and Jawerth, B.. A discrete transform and decompositions of distribution spaces J. Funct. Anal. 93 (1990), 34–170.Google Scholar
[4]Fefferman, C. and Stein, E. M.. Some maximal inequalities. Amer. J. Math. 93 (1971), 107–115.Google Scholar
[5]Han, Y.. Calderón-type reproducing formula and the Tb theorem. Rev. Mat. Iberoamericana 10 (1994), 51–91.Google Scholar
[6]Han, Y., Lee, M.-Y., Lin, C.-C. and Lin, Y.-C.. Calderón–Zygmund operators on product Hardy spaces. J. Funct. Anal. 258 (2010), 2834–2861.Google Scholar
[7]Long, R.-L. and Zhu, X.-X.. L 2-boundedness of some singular integral operators on product domains. Sci. China Ser. A 36 (1993), 538–549.Google Scholar
[8]Journé, J.-L.. Calderón–Zygmund operators on product spaces. Rev. Mat. Iberoamericana 1 (1985), 55–91.Google Scholar
[9]McIntosh, A. and Meyer, Y.. Algèbres d'opérateurs définis par intégrales singulières. C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), 395–397.Google Scholar
[10]Ou, Y.. A T(b) theorem on product spaces. Trans. Amer. Math. Soc. 367 (2015), 6159–6197.Google Scholar