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Lp-multipliers of mixed-norm type on locally compact Vilenkin groups

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

C. W. Onneweer  and
T. S. Quek
C. W. Onneweer
Affiliation:
Department of Mathematics, University of New Mexico, Albuquerque, NM 87131, USA e-mail: onneweer@math.unm.edu
T. S. Quek
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 119260, Republic of Singapore e-mail: matqts@leonis.nus.sg
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Abstract

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Let G be a locally compact Vilenkin group with dual group Γ. We prove Littlewood-Paley type inequalities corresponding to arbitrary coset decompositions of Γ. These inequalities are then applied to obtain new Lp(G) multiplier theorems. The sharpness of some of these results is also discussed.

MSC classification

Secondary: 43A70: Analysis on specific locally compact and other abelian groups 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 3 , December 1998 , pp. 370 - 387
Copyright
Copyright © Australian Mathematical Society 1998

References

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