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On a generalized paraproduct defined by non-convolution

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Part of the Lecture Notes in Mathematics book series (2803,volume 1494)

Abstract

A generalized paraproduct

$$\Pi _b (f)(x) = \int_0^\infty {S_t (b)(x)T_t (f)(x)\frac{{dt}}{t}} $$

is defined, where S t , T t are non-convolution operator families. The main result is that Π b (f) is bounded on L 2(R n) provided b ε BMO (R n).

Keywords

  • Hardy Space
  • Singular Integral Operator
  • Continuous Linear Operator
  • Homogeneous Type
  • Zygmund Operator

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References

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© 1991 Springer-Verlag

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Deng, Dg., Han, Y. (1991). On a generalized paraproduct defined by non-convolution. In: Cheng, MT., Deng, DG., Zhou, XW. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 1494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087755

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  • DOI: https://doi.org/10.1007/BFb0087755

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54901-7

  • Online ISBN: 978-3-540-46474-7

  • eBook Packages: Springer Book Archive