Ball Fractional Integrals

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.