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Sharp interpolation inequalities for discrete operators and applications
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 element...
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Published in: | Bulletin of mathematical sciences 2015-04, Vol.5 (1), p.19-57 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites |
Online Access: | Get full text |
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Summary: | 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. |
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ISSN: | 1664-3607 1664-3615 |
DOI: | 10.1007/s13373-014-0060-8 |