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Generalized poisson integrals and regularity of functions

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Fractional Calculus and Its Applications

Part of the book series: Lecture Notes in Mathematics ((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.

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Authors
  1. Hikosaburo Komatsu
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Bertram Ross

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07161-7

  • Online ISBN: 978-3-540-69975-0

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