The spaces \({\mathfrak L}^\alpha_{p,r}({\mathbb{R}}^{n+1})\) of parabolic potentials
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 \(\alpha =1,2,3...)\).
scientific article; zbMATH DE number 4073414
scientific article