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Preliminaries

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

Abstract

In this chapter, we first recall some basic covering lemmas and notions of doubling cubes, using these we further establish the Lebesgue differentiation theorem and the Calderón–Zygmund decomposition.

Keywords

  • Double Cube
  • Lebesgue Differentiation Theorem
  • Polynomial Growth Condition
  • Besicovitch
  • Nonnegative Radon Measure

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Notes

  1. 1.

    See [23, p. 7].

  2. 2.

    See [121, p. 15].

  3. 3.

    See [137, p. 530] and [37, p. 40].

  4. 4.

    See [111, p. 69].

  5. 5.

    See [157, p. 125].

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Yang, D., Yang, D., Hu, G. (2013). Preliminaries. 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_1

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