Bi-Parametric Potentials, Relevant Function Spaces and Wavelet-Like Transforms

. We introduce new potential type operators , (α > 0, β > 0), and bi-parametric scale of function spaces associated with J α β . These potentials generalize the classical Bessel potentials (for β = 2), and Flett potentials (for β = 1). A characterization of the spaces is given with the aid of a special wavelet–like transform associated with a β-semigroup, which generalizes the well-known Gauss-Weierstrass semigroup (for β = 2) and the Poisson one (for β = 1).