S. S. Volosivets, “Hausdorff Operators on $p$-Adic Linear Spaces and Their Properties in Hardy, $BMO$, and Hölder Spaces”, Mat. Zametki, 2013, Volume 93, Issue 3,Pages 357

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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.

Received: 17.02.2011
Revised: 24.06.2011

DOI: 10.4213/mzm9049