ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.50, no.3, pp.815-824, 2020 (SCI-Expanded)
Classical parabolic Riesz and parabolic Bessel type potentials are interpreted as negative fractional powers of the differential operators (-Delta + partial derivative/partial derivative t) and (I - Delta+ partial derivative/partial derivative t). Here, Delta is the Laplacian and I is the identity operator. We introduce some generalizations of these potentials, namely, we define the family of operators A(beta,theta)(alpha) = (theta I + (-Delta)(beta/2) + partial derivative/partial derivative t)(-alpha) for theta >= 0 and alpha, beta > 0, and investigate its behavior in the framework of L-p (Rn+1)-spaces.