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Title: Multiplicative Systems on Ultra-Metric Spaces
Authors: Memic, Nacima
Keywords: P-adic Derivative
Fourier Multiplier
Multiplicative System
Ultrametric Space
Issue Date: 2010
Publisher: Bulgarian Academy of Sciences - National Committee for Mathematics
Citation: Mathematica Balkanica New Series, Vol. 24, Fasc 3-4 (2010), 275p-284p
Abstract: We perform analysis of certain aspects of approximation in multiplicative systems that appear as duals of ultrametric structures, e.g. in cases of local fields, totally disconnected Abelian groups satisfying the second axiom of countability or more general ultrametric spaces that do not necessarily possess a group structure. Using the fact that the unit sphere of a local field is a Vilenkin group, we introduce a new concept of differentiation in the field of p-adic numbers. Some well known convergence tests are generalized to unbounded Vilenkin groups, i.e. to the setting where the standard boundedness assumption related to the sequence of subgroups generating the underlying topology is absent. A new Fourier multiplier theorem for Hardy spaces on such locally compact groups is obtained. The strong Lq, q > 1, and weak L1 boundedness of Fourier partial sums operators in the system constructed on more general ultrametric spaces is proved.
Description: AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75
ISSN: 0205-3217
Appears in Collections:Mathematica Balkanica New Series, Vol. 24, 2010, Fasc. 3-4

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