Multipliers in dual Sobolev spaces and Schrödinger operators with distribution potentials
type: Item
instance of: scholarly article
title: Multipliers in dual Sobolev spaces and Schrödinger operators with distribution potentials
zbMATH Open document ID: 1029.46029
DOI: 10.1023/A:1015814602021
author: D. Bak
author: A. A. Shkalikov
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: The goal of this paper is to study the multipliers from the Sobolev space \(H^\alpha_p(\mathbb{R}^n)\) to the dual space \(H_{p'}^{-\alpha}(\mathbb{R}^n)\), where \(\alpha\geq 0\), \(p\geq 1\), and \(p,p'\) are Hölder conjugate indices. Here the authors give a complete description of the spaces of multipliers from \(H_p^\alpha (\mathbb{R}^n)\) to \(H_{p'}^{-\alpha} (\mathbb{R}^n)\) (they denote these spaces by \(M^\alpha_p)\) provided that the condition \(\alpha>n/p\) holds. In the case of \(\alpha\leq p/n\) the authors obtain embedding theorems for Sobolev spaces with negative smoothness indices in the spaces \(M^\alpha_p\). The obtained results are applied to define the Schrödinger operator with distribution potentials.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 1928201
zbMATH Keywords: multipliers
zbMATH Keywords: Sobolev space
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: distribution potentials
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1015814602021
OpenAlex ID: W191761582
Recommended article: Multipliers Between Sobolev Spaces
Recommended article: Multipliers in weighted Sobolev spaces
Recommended article: Multipliers of Sobolev spaces in a domain
Recommended article: Operator equations and duality mappings in Sobolev spaces with variable exponents
Recommended article: Multipliers in Hardy-Sobolev spaces
Recommended article: Q5247825
Recommended article: A multiplier theorem for Schrödinger operators
Recommended article: Theory of Sobolev Multipliers
Recommended article: Multiplier operators and extremal functions related to the dual Dunkl-Sonine operator
Recommended article: The multiplication operator in Sobolev spaces with respect to measures
description: scientific article; zbMATH DE number 1928201