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Multipliers for weighted Hardy spaces on locally compact Vilenkin groups

Published online by Cambridge University Press:  17 April 2009

Toshiyuki Kitada
Toshiyuki Kitada
Affiliation:
Department of Mathematics Faculty of General Education, Hirosaki University, Hirosaki 036, Japan
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Let G be a locally compact Vilenkin group. We study multipliers which satisfy a generalised Hörmander condition from power-weighted Hardy space (G) to (G) with 0 < p ≤ q < ∞, 0 < p ≤ 1, −1 < β, β′.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 3 , December 1993 , pp. 441 - 449
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Edwards, R.E. and Gaudry, G.I., Littlewood-Paley and multiplier theory (Springer Verlag, Berlin, Heidelberg, New York, 1977).CrossRefGoogle Scholar
[2]Kitada, T., ‘Weighted Lp multipliers on locally compact Vilenkin groups’, Sci. Rep. Hirosaki Univ. 36 (1989), 135–143.Google Scholar
[3]Kitada, T., ‘Weighted Hp multipliers on locally compact Vilenkin groups’, Monatsh. Math. 110 (1990), 283–295.CrossRefGoogle Scholar
[4]Kitada, T. and Onneweer, C.W., ‘Hörmander-type multipliers on locally compact Vilenkin groups’, in Theory and applications of Gibbs derivatives (Institute of Mathematica, Belgrade, 1989).Google Scholar
[5]Kurtz, D.S., ‘Sharp function estimates for fractional integrals and related operators’, J. Austral. Math. Soc. Ser. A 49 (1990), 129–137.CrossRefGoogle Scholar
[6]Onneweer, C.W. and Quek, T.S., ‘Multipliers on weighted Hardy spaces over locally compact Vilenkin groups, I’, J. Austral. Math. Soc. Ser. A 48 (1990), 472–496.CrossRefGoogle Scholar
[7]Saloff-Coste, L., ‘Opérateurs pseudo diifférentiels sur certains groupes totalement discontinus’, Studia Math. 83 (1986), 205–228.CrossRefGoogle Scholar
[8]Sawyer, E.T. and Wheeden, R.L., ‘Weighted inequalities for fractional integrals on Euclidian spaces and homogeneous spaces’. (Preprint 1989).Google Scholar
[9]Strömberg, J-O. and Wheeden, R.L., ‘Fractional integrals on weighted Hp and Lp spaces’, Trans. Amer. Math. Soc. 287 (1985), 293–321.Google Scholar
[10]Taibleson, M.H., Fourier analysis on local fields, Mathematical Notes 15 (Princeton University Press, 1975).Google Scholar
[11]Vinogradova, G.A., ‘On multipliers in weighted spaces’, Anal. Math. 16 (1990), 215–226.Google Scholar