Fractional integrals for the Weinstein operator

Abstract

In this paper, we study properly the fractional integrals Δw−μ/2, associated with the Weinstein operator, for all μ>0. In the order to give sense to the higher order Riesz Weinstein transforms, we prove that, for a function f∈D∗(Rd) and n=(n1,…,nd)∈Nd∖{(0,…,0)}, Δw−|n|/2 is |n| times differentiable for x outside the support of f and |n|−d times differentiable (if |n|>d) inside the support of f.

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