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The John–Nirenberg Inequality for the Regularized BLO Space on Non-homogeneous Metric Measure Spaces

Part of: Abstract harmonic analysis Harmonic analysis in several variables Set functions, measures and integrals with values in abstract spaces

Published online by Cambridge University Press:  10 December 2019

Haibo Lin ,
Zhen Liu  and
Chenyan Wang
Haibo Lin
Affiliation:
College of Science, China Agricultural University, Beijing100083, People’s Republic of China Email: haibolincau@126.comzhenliucau@163.comchenyanwangcau@126.com
Zhen Liu
Affiliation:
College of Science, China Agricultural University, Beijing100083, People’s Republic of China Email: haibolincau@126.comzhenliucau@163.comchenyanwangcau@126.com
Chenyan Wang
Affiliation:
College of Science, China Agricultural University, Beijing100083, People’s Republic of China Email: haibolincau@126.comzhenliucau@163.comchenyanwangcau@126.com
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Abstract

Let $({\mathcal{X}},d,\unicode[STIX]{x1D707})$ be a metric measure space satisfying the geometrically doubling condition and the upper doubling condition. In this paper, the authors establish the John-Nirenberg inequality for the regularized BLO space $\widetilde{\operatorname{RBLO}}(\unicode[STIX]{x1D707})$.

Keywords

non-homogeneous metric measure spaceJohn–Nirenberg inequalitythe space ˜RBLO(𝜇)

MSC classification

Primary: 43A99: None of the above, but in this section
Secondary: 42B35: Function spaces arising in harmonic analysis 28B99: None of the above, but in this section
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020 , pp. 643 - 654
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

Z. L. is the corresponding author. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11471042).

References

Bui, T. A. and Duong, X. T., Hardy spaces, regularized BMO spaces and the boundedness of Calderón-Zygmund operators on non-homogeneous spaces. J. Geom. Anal. 23(2013), 895–932. https://doi.org/10.1007/s12220-011-9268-yCrossRefGoogle Scholar
Coifman, R. R. and Rochberg, R., Another characterization of BMO. Proc. Am. Math. Soc. 79(1980), 249–254. https://doi.org/10.1090/s0002-9939-1980-0565349-8CrossRefGoogle Scholar
Coifman, R. R. and Weiss, G., Analyse harmonique non-commutative sur certains espaces homogènes. Étude de Certaines Intégrales Singulières, Lecture Notes in Mathematics, 242, Springer-Verlag, Berlin–New York, 1971. https://doi.org/10.1007/bfb0058953.CrossRefGoogle Scholar
Coifman, R. R. and Weiss, G., Extensions of Hardy spaces and their use in analysis. Bull. Am. Math. Soc. 83(1977), 569–645. https://doi.org/10.1515/9781400827268.295CrossRefGoogle Scholar
Duoandikoetxea, J., Fourier analysis. Graduate Studies in Mathematics, 29, American Mathematical Society, Providence, RI, 2001. https://doi.org/10.1090/gsm/029Google Scholar
Fu, X., Lin, H., Yang, D., and Yang, D., Hardy spaces H p over non-homogeneous metric measure spaces and their applications. Sci. China Math. 58(2015), 309–388. https://doi.org/10.1007/s11425-014-4956-2CrossRefGoogle Scholar
Fu, X., Yang, D., and Yang, D., The molecular characterization of the Hardy space H 1 on non-homogeneous metric measure spaces and its application. J. Math. Anal. Appl. 410(2014), 1028–1042. https://doi.org/10.1016/j.jmaa.2013.09.021CrossRefGoogle Scholar
Heinonen, J., Lectures on analysis on metric spaces. Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4613-0131-8CrossRefGoogle Scholar
Hytönen, T., A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa. Publ. Mat. 54(2010), 485–504. https://doi.org/10.5565/publmat_54210_10CrossRefGoogle Scholar
Hytönen, T., Yang, D., and Yang, D., The Hardy space H 1 on non-homogeneous metric spaces. Math. Proc. Cambridge Philos. Soc. 153(2012), 9–31. https://doi.org/10.1017/s0305004111000776CrossRefGoogle Scholar
Jiang, Y., Spaces of type BLO for non-doubling measures. Proc. Am. Math. Soc. 133(2005), 2101–2107. https://doi.org/10.1090/s0002-9939-05-07795-6CrossRefGoogle Scholar
John, F. and Nirenberg, L., On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14(1961), 415–426. https://doi.org/10.1007/978-1-4612-5412-6_36CrossRefGoogle Scholar
Lin, H. and Yang, D., Spaces of type BLO on non-homogeneous metric measure. Front. Math. China 6(2011), 271–292. https://doi.org/10.1007/s11464-011-0098-9CrossRefGoogle Scholar
Lin, H., Nakai, E., and Yang, D., Boundedness of Lusin-area and g 𝜆∗ functions on localized BMO spaces over doubling metric measure spaces. Bull. Sci. Math. 135(2011), 59–88. https://doi.org/10.1155/2011/187597CrossRefGoogle Scholar
Tolsa, X., BMO, H 1, and Calderón-Zygmund operators for non doubling measures. Math. Ann. 319(2001), 89–149. https://doi.org/10.1007/pl00004432Google Scholar
Wang, D., Zhou, J., and Teng, Z., Some characterizations of BLO space. Math. Nachr. 291(2018), 1908–1918. https://doi.org/10.1002/mana.201700318CrossRefGoogle Scholar
Yang, D., Yang, D., and Fu, X., The Hardy space H 1 on non-homogeneous spaces and its applications–a survey. Eurasian Math. J. 4(2013), 104–139.Google Scholar
Yang, D., Yang, D., and Hu, G., The Hardy space H 1 with non-doubling measures and their applications. Lecture Notes in Mathematics, 2084, Springer, Cham, 2013. https://doi.org/10.1007/978-3-319-00825-7_3CrossRefGoogle Scholar