Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1340

 Title: Multiplicative Systems on Ultra-Metric Spaces Authors: Memic, Nacima Keywords: P-adic DerivativeFourier MultiplierMultiplicative SystemUltrametric 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 URI: http://hdl.handle.net/10525/1340 ISSN: 0205-3217 Appears in Collections: Mathematica Balkanica New Series, Vol. 24, 2010, Fasc. 3-4

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