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Multipliers on weighted Hardy spaces over locally compact Vilenkin groups, I

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 and Statistics University of New MexicoAlbuquerque, New Mexico 87131, U.S.A.
T. S. Quek
Affiliation:
Department of Mathematics National University of SingaporeSingapore 0511 Republic of, Singapore
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Abstract

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Let G denote a locally compact Vilenkin group with dual group Γ. We give sufficient conditions for a function ϕ ∈ L∞ (Γ) to be a multiplier from the power-weighted Hardy space to itself or the corresponding power-weighted Lebesgue space

MSC classification

Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A70: Analysis on specific locally compact and other abelian groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 3 , June 1990 , pp. 472 - 496
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Coifman, R. and Weiss, G., ‘Extensions of Hardy spaces and their use in analysis,’ Bull. Amer. Math. Soc. 83 (1977), 569–645.CrossRefGoogle Scholar
[2]Edwards, R. E. and Gaudry, G. I., Littlewood-Paley and multiplier theory, (Springer-Verlag, Berlin, 1977).CrossRefGoogle Scholar
[3]Garcia-Cuerva, J. and Rubio de Francia, J. L., Weighted norm inequalities and related topics, (North-Holland Mathematics Studies 116, North-Holland, Amsterdam, 1985).Google Scholar
[4]Kitada, T., ‘Hp-multiplier theorems on certain totally disconnected groups’, Sci. Rep. Hirosaki Univ. 34 (1987), 1–7.Google Scholar
[5]Kitada, T., ‘Multipliers on weighted Hardy spaces over certain totally disconnected groups’, Internal. J. Math. Math. Sci. 11 (1988), 665–675.CrossRefGoogle Scholar
[6]Kitada, T., ‘Hp multiplier theorem on certain totally disconnected groups, II’, preprint.Google Scholar
[7]Onneweer, C. W., ‘Multipliers on weighted Lp-spaces over certain totally disconnected groups’, Trans. Amer. Math. Soc. 288 (1985), 347–357.Google Scholar
[8]Onneweer, C. W. and Quek, T. S., ‘Multipliers on weighted Lp-spaces over locally compact Vilenkin groups’, Proc. Amer. Math. Soc. 105 (1989), 622–631.Google Scholar
[9]Onneweer, C. W. and Quek, T. S., ‘Hp multiplier results on locally compact Vilenkin groups’, Quart. J. Math. Oxford Ser. (2) 40 (1989), 313–323.CrossRefGoogle Scholar
[10]Taibleson, M. H., ‘Harmonic analysis on n-dimensional vector spaces over local fields, III. Multipliers’, Math. Ann. 187 (1970), 259–271.CrossRefGoogle Scholar
[11]Taibleson, M. H., Fourier analysis on local fields, (Mathematical Notes 15, Princeton University Press, 1975).Google Scholar
[12]Taibleson, M. H. and Weiss, G., The molecular characterization of certain Hardy spaces, (Astérisque 77, pp. 68–149, 1980).Google Scholar
[13]Vilenkin, N. Ya., On a class of complete orthonormal systems, (Amer. Math. Soc. Transl. (2) 28, pp. 1–35, 1963).Google Scholar