Title: Lipschitz continuity properties for p-adic semi-algebraic and subanalytic functions
Authors: Cluckers, Raf ×
Comte, Georges
Loeser, Francois #
Issue Date: Jun-2010
Publisher: Birkhauser verlag ag
Series Title: Geometric and functional analysis vol:20 issue:1 pages:68-87
Abstract: We prove that a (globally) subanalytic function f : X subset of Q(p)(n) -> Q(p) which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken to be subanalytic. We also prove the analogous result for a subanalytic family of functions f(y) : X-y subset of Q(p)(n) -> Q(p) depending on p-adic parameters. The statements also hold in a semi-algebraic set-up and also in a finite field extension of Q(p). These results are p-adic analogues of results of K. Kurdyka over the real numbers. To encompass the total disconnectedness of p-adic fields, we need to introduce new methods adapted to the p-adic situation.
ISSN: 1016-443X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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