Geodesic
Hilbert inequality for vector valued functions
Archivum mathematicum, Tome 47 (2011) no. 3, pp. 229-243.

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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 $.
Classification : 26D15
Keywords: Hardy-Hilbert’s integral inequality; $\beta $-function; Hölder’s inequality 
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     author = {Das, Namita and Sahoo, Srinibas},
     title = {Hilbert inequality for vector valued functions},
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     pages = {229--243},
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     volume = {47},
     number = {3},
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     zbl = {1249.26033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2011__47_3_a4/}
}
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Das, Namita; Sahoo, Srinibas. Hilbert inequality for vector valued functions. Archivum mathematicum, Tome 47 (2011) no. 3, pp. 229-243. http://geodesic.mathdoc.fr/item/ARM_2011__47_3_a4/