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Generalized poisson integrals and regularity of functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 457)

Abstract

The classical Poisson integral may be regarded as the semigroup of operators generated by - √−Δ. The author shows that −Δ may be replaced by a wider class of elliptic operators and extends Hardy's theory saying that the regularity of a function is measured by the behavior of the Poisson integral.

The theory of fractional powers of non-negative operators plays an essential role.

Keywords

  • Banach Space
  • Elliptic Operator
  • Besov Space
  • Fractional Power
  • Infinitesimal Generator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1975 Springer-Verlag

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Komatsu, H. (1975). Generalized poisson integrals and regularity of functions. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067108

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  • DOI: https://doi.org/10.1007/BFb0067108

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  • Print ISBN: 978-3-540-07161-7

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