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Boundedness of Operators over \(({\mathbb{R}}^{D},\mu )\)

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The Hardy Space H1 with Non-doubling Measures and Their Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2084))

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Abstract

In this chapter, we focus our attention on the boundedness of singular integral operators in the Lebesgue space and the Hardy space over \(({\mathbb{R}}^{D},\mu )\). We first establish some weighted estimates for local sharp maximal operator as well as several interpolation results which are useful in applications. Then we investigate the boundedness of singular integral operators on L p(μ) and H 1(μ), and the boundedness of maximal singular integral operators and commutators on L p(μ) as well as their endpoint estimates.

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Notes

  1. 1.

    See [121].

  2. 2.

    See [6, II, p. 33].

  3. 3.

    See [121].

  4. 4.

    See [108].

  5. 5.

    See [109] for the details.

  6. 6.

    See [108].

  7. 7.

    See [108].

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education, Beijing, People’s Republic of China

    Dachun Yang

  2. School of Mathematical Sciences, Xiamen University, Xiamen, People’s Republic of China

    Dongyong Yang

  3. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, People’s Republic of China

    Guoen Hu

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  1. Dachun Yang
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  2. Dongyong Yang
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  3. Guoen Hu
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Yang, D., Yang, D., Hu, G. (2013). Boundedness of Operators over \(({\mathbb{R}}^{D},\mu )\) . In: The Hardy Space H1 with Non-doubling Measures and Their Applications. Lecture Notes in Mathematics, vol 2084. Springer, Cham. https://doi.org/10.1007/978-3-319-00825-7_5

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