The Hardy Inequality for Hermite Expansions
The purpose of the paper is to prove a sharp form of Hardy-type inequality, conjectured by Kanjin, for Hermite expansions of functions in the Hardy space H 1 ( R ) , that is, ∑ n = 1 ∞ n - 3 4 | a n ( f ) | ≤ A ‖ f ‖ H 1 ( R ) for all f ∈ H 1 ( R ) , where A is a constant independent of f ....
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| Veröffentlicht in: | The Journal of fourier analysis and applications 2015-04, Vol.21 (2), p.267-280 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The purpose of the paper is to prove a sharp form of Hardy-type inequality, conjectured by Kanjin, for Hermite expansions of functions in the Hardy space
H
1
(
R
)
, that is,
∑
n
=
1
∞
n
-
3
4
|
a
n
(
f
)
|
≤
A
‖
f
‖
H
1
(
R
)
for all
f
∈
H
1
(
R
)
, where
A
is a constant independent of
f
. |
|---|---|
| ISSN: | 1069-5869 1531-5851 |
| DOI: | 10.1007/s00041-014-9367-9 |