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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© 2002 Springer Science+Business Media Dordrecht
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Edmunds, D.E., Kokilashvili, V., Meskhi, A. (2002). Ball Fractional Integrals. In: Bounded and Compact Integral Operators. Mathematics and Its Applications, vol 543. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9922-1_4
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DOI: https://doi.org/10.1007/978-94-015-9922-1_4
Publisher Name: Springer, Dordrecht
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