Sharp interpolation inequalities for discrete operators and applications

Ilyin, A, Laptev, A and Zelik, S (2015) Sharp interpolation inequalities for discrete operators and applications BULLETIN OF MATHEMATICAL SCIENCES, 5 (1). pp. 19-57.

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Abstract

We consider interpolation inequalities for imbeddings of the l 2-sequence spaces over d-dimensional lattices into the l ∞ 0 spaces written as interpolation inequality between the l 2-norm of a sequence and its difference. A general method is developed for finding sharp constants, extremal elements and correction terms in this type of inequalities. Applications to Carlson’s inequalities and spectral theory of discrete operators are given

Item Type:	Article
Subjects :	Mathematics
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Ilyin, A, Laptev, A and Zelik, S
Date :	April 2015
DOI :	10.1007/s13373-014-0060-8
Copyright Disclaimer :	© The Author(s) 2014. This article is published with open access at SpringerLink.com
Uncontrolled Keywords :	Discrete operators, Sobolev inequality, Interpolation inequalities, Green's function, Sharp constants, Lieb-Thirring inequalities, Carlson inequality
Related URLs :	Author
Depositing User :	Symplectic Elements
Date Deposited :	03 Nov 2016 11:33
Last Modified :	31 Oct 2017 18:43
URI:	http://epubs.surrey.ac.uk/id/eprint/812219

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