Sharp interpolation inequalities for discrete operators and applications
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Published version
Author(s)
Ilyin, A
Laptev, A
Zelik, S
Type
Journal Article
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.
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.
Date Issued
2014-10-26
Date Acceptance
2014-10-11
Citation
Bulletin of Mathematical Sciences, 2014, 5 (1), pp.19-57
ISSN
1664-3615
Publisher
SpringerOpen
Start Page
19
End Page
57
Journal / Book Title
Bulletin of Mathematical Sciences
Volume
5
Issue
1
Copyright Statement
© The Author(s) 2014. This article is published with open access at SpringerLink.com
License URL
Subjects
Science & Technology
Physical Sciences
Mathematics
Discrete operators
Sobolev inequality
Interpolation inequalities
Green's function
Sharp constants
Lieb-Thirring inequalities
Carlson inequality
LIEB-THIRRING INEQUALITIES
CONSTANTS
Publication Status
Published