The spaces \({\mathfrak L}^\alpha_{p,r}({\mathbb{R}}^{n+1})\) of parabolic potentials (Q1110688)

Anisotropic Lebesgue spaces \[ {\mathfrak L}^{\alpha}_{p,r}({\mathbb{R}}^{n+1})=\{f: f\in L_ r({\mathbb{R}}^{n+1}),\quad {\mathcal F}^{-1}(| \xi |^ 2+i\tau)^{\alpha /2} {\mathcal F}f\in L_ p({\mathbb{R}}^{n+1})\} \] which are closely connected with Jones-Sampson classes of parabolic potentials are introduced. These spaces are described in terms of partial Riesz derivatives and partial Riesz potentials. Some applications of this description are given (multipliers in \({\mathfrak L}^{\alpha}_{p,r}\), identification with Sobolev-type spaces for \(\alpha =1,2,3...)\).