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A Note on H1 Multipliers for Locally Compact Vilenkin Groups

Published online by Cambridge University Press:  20 November 2018

James E. Daly
Affiliation:
Department of Mathematics University of Colorado Colorado Springs, CO 80907 USA, email: jedaly@math.uccs.edu
Keith L. Phillips
Affiliation:
Department of Mathematics University of Colorado Colorado Springs, CO 80907 USA, email: keith@pyramid.uccs.edu
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Abstract

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Kitada and then Onneweer and Quek have investigated multiplier operators on Hardy spaces over locally compact Vilenkin groups. In this note, we provide an improvement to their results for the Hardy space ${{H}^{1}}$ and provide examples showing that our result applies to a significantly larger group of multipliers.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Chao, J. A. and Janson, S., A Note on H1 q-martingales. Pacific J. Math. 92 (1981), 307317.Google Scholar
2. Daly, J. and Phillips, K., Walsh Multipliers and Square Functions for Hardy Spaces. Acta Math. Hungar. (4) 79 (1998), 311327.Google Scholar
3. Daly, J. and Phillips, K., On Singular Integrals, Multipliers, H1, and Fourier Series—a Local Field Phenomenon. Math. Ann. 265 (1983), 181219.Google Scholar
4. Kitada, T., Hp Multiplier Theorems on Certain Totally Disconnected Groups. Sci. Rep. Hirosaki Univ. 34 (1987), 17.Google Scholar
5. Onneweer, C. W. and Quek, T. S., Hp Multiplier Results on Locally Compact Vilenkin Groups. Quart. J. Math. Oxford Ser. 2 40 (1989), 313323.Google Scholar
6. Simon, P., (L1, H)-Type Estimations for Some Operators with respect to the Walsh-Paley Systems. Acta. Math. Hungar. (3–4) 46 (1985), 307310.Google Scholar
7. Young, W. S., Littlewood-Paley and Multiplier Theorems for Vilenkin-Fourier Series. Canad. J.Math (4) 46 (1994), 662672.Google Scholar
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