The spaces \({\mathfrak L}^\alpha_{p,r}({\mathbb{R}}^{n+1})\) of parabolic potentials
type: Item
instance of: scholarly article
title: The spaces \({\mathfrak L}^\alpha_{p,r}({\mathbb{R}}^{n+1})\) of parabolic potentials
zbMATH Open document ID: 0657.31017
DOI: 10.1007/BF01909436
author: V. Nogin
author: Boris Rubin
published in: Analysis Mathematica
publication date: 1987-01-01T00:00:00Z
review text: 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 \(\alpha =1,2,3...)\).
Mathematics Subject Classification ID: 31C15
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 4073414
zbMATH Keywords: Anisotropic Lebesgue spaces
zbMATH Keywords: parabolic potentials
zbMATH Keywords: partial Riesz derivatives
zbMATH Keywords: partial Riesz potentials
zbMATH Keywords: multipliers
MaRDI profile type: Publication
cites work: Lebesgue spaces of parabolic potentials
cites work: Parabolic potentials with support on a half-space
cites work: Hypersingular Integrals and Parabolic Potentials
cites work: Period, index and potential \(\text Ш\)
cites work: A Characterization of Parabolic Function Spaces
cites work: Parabolic Function Spaces With Mixed Norm
cites work: Q4397397
cites work: Q3506242
cites work: Stone Duality for Nominal Boolean Algebras with И
cites work: The Brauer-Manin Obstruction and III[2]
cites work: Q3435035
cites work: Q5522602
cites work: Q5557358
description: scientific article; zbMATH DE number 4073414