Hilbert inequality for vector valued functions
Archivum Mathematicum (2011)
- Volume: 047, Issue: 3, page 229-243
- ISSN: 0044-8753
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topDas, Namita, and Sahoo, Srinibas. "Hilbert inequality for vector valued functions." Archivum Mathematicum 047.3 (2011): 229-243. <http://eudml.org/doc/246253>.
@article{Das2011,
abstract = {In this paper we consider a class of Hankel operators with operator valued symbols on the Hardy space $\{ \mathcal \{H\}\}_\{\Xi \}^2(\mathbb \{T\})$ where $\Xi $ is a separable infinite dimensional Hilbert space and showed that these operators are unitarily equivalent to a class of integral operators in $L^2(0, \infty )\otimes \Xi .$ We then obtained a generalization of Hilbert inequality for vector valued functions. In the continuous case the corresponding integral operator has matrix valued kernels and in the discrete case the sum involves inner product of vectors in the Hilbert space $\Xi $.},
author = {Das, Namita, Sahoo, Srinibas},
journal = {Archivum Mathematicum},
keywords = {Hardy-Hilbert’s integral inequality; $\beta $-function; Hölder’s inequality; Hardy-Hilbert's integral inequality; -function; Hölder’s inequality},
language = {eng},
number = {3},
pages = {229-243},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Hilbert inequality for vector valued functions},
url = {http://eudml.org/doc/246253},
volume = {047},
year = {2011},
}
TY - JOUR
AU - Das, Namita
AU - Sahoo, Srinibas
TI - Hilbert inequality for vector valued functions
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 3
SP - 229
EP - 243
AB - In this paper we consider a class of Hankel operators with operator valued symbols on the Hardy space ${ \mathcal {H}}_{\Xi }^2(\mathbb {T})$ where $\Xi $ is a separable infinite dimensional Hilbert space and showed that these operators are unitarily equivalent to a class of integral operators in $L^2(0, \infty )\otimes \Xi .$ We then obtained a generalization of Hilbert inequality for vector valued functions. In the continuous case the corresponding integral operator has matrix valued kernels and in the discrete case the sum involves inner product of vectors in the Hilbert space $\Xi $.
LA - eng
KW - Hardy-Hilbert’s integral inequality; $\beta $-function; Hölder’s inequality; Hardy-Hilbert's integral inequality; -function; Hölder’s inequality
UR - http://eudml.org/doc/246253
ER -
References
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