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Mat. Zametki, 2013, Volume 93, Issue 3, Pages 357–367 (Mi mz9049)  

This article is cited in 6 scientific papers (total in 6 papers)

Hausdorff Operators on $p$-Adic Linear Spaces and Their Properties in Hardy, $BMO$, and Hölder Spaces

S. S. Volosivets

Saratov State University named after N. G. Chernyshevsky

Abstract: Sufficient conditions for the boundedness of $p$-adic matrix operators in Hardy, Hölder and $BMO$ spaces are obtained. These conditions are expressed in terms of the determinant of the matrix and its norm in a $p$-adic linear space.

Keywords: Hausdorff operator, $p$-adic linear space, Hardy space, Hölder space, the space $BMO$, $p$-adic matrix operator, Haar measure.

DOI: https://doi.org/10.4213/mzm9049

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English version:
Mathematical Notes, 2013, 93:3, 382–391

Bibliographic databases:

Received: 17.02.2011
Revised: 24.06.2011

Citation: S. S. Volosivets, “Hausdorff Operators on $p$-Adic Linear Spaces and Their Properties in Hardy, $BMO$, and Hölder Spaces”, Mat. Zametki, 93:3 (2013), 357–367; Math. Notes, 93:3 (2013), 382–391

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Platonov, “Some problems in the theory of approximation of functions on the group of $p$-adic numbers”, P-Adic Numbers Ultrametric Anal. Appl., 10:2 (2018), 118–129  crossref  mathscinet  isi
    2. S. S. Volosivets, M. A. Kuznetsova, “Generalized $p$-adic Fourier transform and estimates of integral modulus of continuity in terms of this transform”, P-Adic Numbers Ultrametric Anal. Appl., 10:4 (2018), 312–321  crossref  mathscinet  isi  scopus
    3. Sarfraz N., Hussain A., “Estimates For the Commutators of P-Adic Hausdorff Operator on Herz-Morrey Spaces”, Mathematics, 7:2 (2019), 127  crossref  mathscinet  isi  scopus
    4. Chuong N.M., Duong D.V., Dung K.H., “Some Estimates For P-Adic Rough Multilinear Hausdorff Operators and Commutators on Weighted Morrey-Herz Type Spaces”, Russ. J. Math. Phys., 26:1 (2019), 9–31  crossref  mathscinet  isi  scopus
    5. Platonov S.S., “Some Problems in the Theory of Approximation of Functions on Locally Compact Vilenkin Groups”, P-Adic Numbers Ultrametric Anal. Appl., 11:2 (2019), 163–175  crossref  isi
    6. Nguen Min Chyong, Dao Van Dyong, Nguen Dyk Duet, “Vesovye otsenki kommutatorov dlya operatorov Khausdorfa na gruppe Geizenberga”, Izv. vuzov. Matem., 2020, no. 2, 39–62  mathnet  crossref
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