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Ball Fractional Integrals

  • David E. Edmunds
  • Vakhtang Kokilashvili
  • Alexander Meskhi
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 543)

Abstract

A new class of fractional integrals connected with balls in R n was introduced and investigated by B. Rubin in [246] (see also [247]). The special interest in ball fractional integrals (BFI’s) arises from the fact that Riesz potentials I a f over a ball B may be represented by a composition of such integrals. This enables one to derive necessary and sufficient solvability conditions for the equation Iαφ = f in Lebesgue spaces with power weights and to construct the solution in closed form.

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • David E. Edmunds
    • 1
  • Vakhtang Kokilashvili
    • 1
  • Alexander Meskhi
    • 2
  1. 1.Centre for Mathematical Analysis and its ApplicationUniversity of SussexSussexUK
  2. 2.A. Razmadze Mathematical InstituteGeorgian Academy of SciencesTbilisiGeorgia

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