Boundedness of <i>θ</i>-type Calderón-Zygmund operators on non-homogeneous metric measure space

doi:10.1007/s11464-015-0464-0

Front. Math. China

2016, Vol. 11

Issue (1) : 141-153 https://doi.org/10.1007/s11464-015-0464-0

RESEARCH ARTICLE

Boundedness of θ-type Calderón-Zygmund operators on non-homogeneous metric measure space

Chol RI¹,Zhenqiu ZHANG^2,^*(

)

1. Department of Mathematics, Kim Hyong Jik Normal University, PyongYang, DPR Korea
2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

Download: PDF(137 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Let (X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hytönen. Under this assumption, we prove thatθ-type Calderón-Zygmund operators which are bounded on L²(μ) are also bounded from L^∞(μ) into RBMO(μ) and from H^1,∞_at (μ) into L¹(μ).

Keywords Non-homogeneous spaces θ-type Calderón-Zygmund operators RBMO(μ) space H¹ ^,∞_at (μ) space

Corresponding Author(s): Zhenqiu ZHANG

Issue Date: 02 December 2015

Cite this article:

Chol RI,Zhenqiu ZHANG. Boundedness of θ-type Calderón-Zygmund operators on non-homogeneous metric measure space[J]. Front. Math. China, 2016, 11(1): 141-153.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0464-0
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I1/141

1	Bui T A, Duong X T. Hardy spaces, regularized BMO spaces and the boundedness of Calderón-Zygmund operators on non-homogeneous spaces. J Geom Anal, 2013, 23: 895–932 https://doi.org/10.1007/s12220-011-9268-y
2	Coifman R, Weiss G. Analyse Harmonique Non-Commutative sur Certains Espaces Homogenes. Lecture Notes in Math, Vol 242. Berlin: Springer, 1971
3	Coifman R, Weiss G. Extensions of Hardy spaces and their use in analysis. Bull Amer Math Soc, 1977, 83: 569–645 https://doi.org/10.1090/S0002-9904-1977-14325-5
4	Fu X, Hu G, Yang D. A remark on the boundedness of Calderón-Zygmund operators in non-homogeneous spaces. Acta Math Sin (Engl Ser), 2007, 23: 449–456 https://doi.org/10.1007/s10114-005-0723-1
5	Heinenon J. Lectures on Analysis on Metric Spaces. New York: Springer-Verlag, 2001 https://doi.org/10.1007/978-1-4613-0131-8
6	Hytönen T. A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa. Publ Mat, 2010, 54: 485–504 https://doi.org/10.5565/PUBLMAT_54210_10
7	Hytönen T, Liu S, Yang D, Yang D. Boundedness of Calderón-Zygmund operators on non-homogeneous metric measure spaces. Canad J Math, 2012, 64: 892–923 https://doi.org/10.4153/CJM-2011-065-2
8	Hytönen T, Yang D, Yang D. The Hardy space H1 on non-homogeneous metric spaces. Math Proc Cambridge Philos Soc, 2012, 153: 9–31 https://doi.org/10.1017/S0305004111000776
9	Lin H, Yang D. Spaces of type BLO on non-homogeneous metric measure spaces. Front Math China, 2011, 6: 271–292 https://doi.org/10.1007/s11464-011-0098-9
10	Liu S, Yang D, Yang D. Boundedness of Calderón-Zygmund operators on nonhomogeneous metric measure spaces: equivalent characterizations. J Math Anal Appl, 2012, 386: 258–272 https://doi.org/10.1016/j.jmaa.2011.07.055
11	Nazarov F, Treil S, Volberg A. The Tb-theorem on non-homogeneous spaces. Acta Math, 2003, 190: 151–239 https://doi.org/10.1007/BF02392690
12	Tolsa X. BMO, H1 and Caldeŕon-Zygmund operators for non doubling measures. Math Ann, 2001, 319: 89–149 https://doi.org/10.1007/PL00004432
13	Xie R, Shu L. θ-type Caldeŕon-Zygmund operators with non-doubling measures. Acta Math Appl Sin Engl Ser, 2013, 29(2): 263–280 https://doi.org/10.1007/s10255-013-0217-3
14	Yabuta K. Generalization of Calderón-Zygmund operators. Studia Math, 1985, 82: 17–31
15	Yang D, Yang D, Hu G. The Hardy space H1 with non-doubling measures and their applications. Lecture Notes in Math, Vol 2084. Berlin: Springer, 2013 https://doi.org/10.1007/978-3-319-00825-7

Viewed

Full text

Abstract

Cited

Shared

Discussed