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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Calderón-Zygmund operators on Hardy spaces without the doubling condition

Author(s): Wengu Chen; Yan Meng; Dachun Yang
Journal: Proc. Amer. Math. Soc. 133 (2005), 2671-2680.
MSC (2000): Primary 42B20; Secondary 42B30, 42B25, 43A99
Posted: March 17, 2005
MathSciNet review: 2146213
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Abstract | References | Similar articles | Additional information

Abstract: Let $\mu$ be a non-negative Radon measure on $\mathbb{R}^d$ which only satisfies some growth condition. In this paper, the authors obtain the boundedness of Calderón-Zygmund operators in the Hardy space $H^1(\mu)$.

References:

[1]
G. Hu, Y. Meng and D. Yang, New atomic characterization of $H^1$ space with non-doubling measures and its applications, Math. Proc. Camb. Phil. Soc. to appear.

[2]
F. Nazarov, S. Treil and A. Volberg, Cauchy integral and Calderón-Zygmund operators on nonhomogeneous spaces, Internat. Math. Res. Notices 15 (1997), 703-726. MR 1470373 (99e:42028)

[3]
F. Nazarov, S. Treil and A. Volberg, Accretive system $Tb$-theorems on nonhomogeneous spaces, Duke Math. J. 113 (2002), 259-312. MR 1909219 (2003g:42030)

[4]
F. Nazarov, S. Treil and Volberg, The $Tb$-theorem on non-homogeneous spaces, Acta Math. 190 (2003), 151-239. MR 1998349

[5]
X. Tolsa, BMO, $H^1$ and Calderón-Zygmund operators for non doubling measures, Math. Ann. 319 (2001), 89-149. MR 1812821 (2002c:42029)

[6]
X. Tolsa, Littlewood-Paley theory and the $T(1)$ theorem with non-doubling measures, Adv. Math. 164 (2001), 57-116. MR 1870513 (2003e:42029)

[7]
X. Tolsa, A proof of the weak $(1,\,1)$inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition, Publ. Mat. 45 (2001), 163-174. MR 1829582 (2002d:42019)
[8]
X. Tolsa, The space $H^1$ for nondoubling measures in terms of a grand maximal operator, Trans. Amer. Math. Soc. 355 (2003), 315-348. MR 1928090 (2003e:42030)

[9]
X. Tolsa, Painlevé's problem and the semiadditivity of analytic capacity, Acta Math. 190 (2003), 105-149. MR 1982794

[10]
J. Verdera, The fall of the doubling condition in Calderón-Zygmund theory, Publ. Mat. 2002, Vol. Extra, 275-292. MR 1964824 (2004b:42035)

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Additional Information:

Wengu Chen
Affiliation: Institute of Applied Physics and Computational Mathematics, P.O. 8009, Beijing, 100088, People's Republic of China
Email: chenwg@mail.iapcm.ac.cn

Yan Meng
Affiliation: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People's Republic of China
Email: mengyan@mail.bnu.edu.cn

Dachun Yang
Affiliation: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People's Republic of China
Email: dcyang@bnu.edu.cn

DOI: 10.1090/S0002-9939-05-07781-6
PII: S 0002-9939(05)07781-6
Received by editor(s): March 8, 2004
Received by editor(s) in revised form: April 22, 2004
Posted: March 17, 2005
Additional Notes: This project was supported by NNSF (No. 10271015 & No. 10371080) of China and the third (corresponding) author was also supported by RFDP (No. 20020027004) of China.
Communicated by: Andreas Seeger
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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