A generalization of parabolic potentials associated to Laplace–Bessel differential operator and its behavior in the weighted Lebesque spaces

Abstract

In this work we introduce some generalizations of the singular parabolic Riesz and parabolic Bessel potentials. Namely, ∆ν being the Laplace–Bessel singular differential operator, we define the families of operators H α β,ν = ( ∂ ∂t + (−∆ν) β/2 )−α/β and H α β,ν = ( I + ∂ ∂t + (−∆ν) β/2 )−α/β , (α, β > 0), and investigate their properties in the special weighted Lp,ν -spaces.