The Space of Weighted Bessel Potentials

A fractional weighted integro-differentiation operator is considered. The kernel of this operator is determined by applying the Fourier–Bessel integral transform. The space of weighted Bessel potentials is described on the basis of the Stein–Lizorkin approach; the description uses B-hypersingular integrals and weighted Riesz potentials that were introduced earlier by one of the authors.