Geodesic
Characteristic of UMD spaces with Hilbert transformation of vector-valued functions on the field of $p$-adic numbers
Problemy fiziki, matematiki i tehniki, no. 1 (2011), pp. 79-83

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We consider Hilbert transformation of vector-valued functions on the group of $p$-adic integers $Z_p$ taking values in Banach space $X$ , and square-integrable in Bochner sense. If Hilbert transformation $H \colon L_2(Z_p, X) \to L_2(Z_p, X)$ with $p \ne 2$ is a bounded operator, then Banach space $X$ is an UMD space.
Mots-clés : Hilbert transformation, Fourier transformation.
Keywords: UMD space, $p$-adic numbers 
@article{PFMT_2011_1_a12,
     author = {A. G. Sidoryk},
     title = {Characteristic of {UMD} spaces with {Hilbert} transformation of vector-valued functions on the field of $p$-adic numbers},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {79--83},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2011_1_a12/}
}
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A. G. Sidoryk. Characteristic of UMD spaces with Hilbert transformation of vector-valued functions on the field of $p$-adic numbers. Problemy fiziki, matematiki i tehniki, no. 1 (2011), pp. 79-83. http://geodesic.mathdoc.fr/item/PFMT_2011_1_a12/