Characterization of some function spaces in terms of hypersingular integrals

C H A P T E R 7

Since the hypersingular integral with the constant characteristic generates an operator inverse to the Riesz potential operator according to Theorem 3.19, it is natural to describe the space of Riesz potentials, with densities in Lp(R

n), in terms of convergence of hypersingular integrals. The space of the well known Bessel potentials is also described in such terms.