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BMO and singular integrals over local fields

Part of: Harmonic analysis in several variables Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

James E. Daly  and
Douglas S. Kurtz
James E. Daly
Affiliation:
Department of Mathematics, University of Colorado, Colorado Springs, Colorado, 80933, USA
Douglas S. Kurtz
Affiliation:
Department of Mathematical Science, New Mexico State University, Las Cruces, New Mexico 88003, USA
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Abstract

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This paper is concerned with the behavior of certain principal-value, singular integral operators on L∞ and BMO defined over a local field. It is shown that unless the definition of these operators is changed appropriately, they may not be defined for some function in these spaces. Direct, constructive proofs of the existence and boundedness of the altered operators under certain smoothness conditions on the kernel are given.

MSC classification

Secondary: 43A70: Analysis on specific locally compact and other abelian groups 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B30: $H^p$-spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 3 , June 1993 , pp. 321 - 333
Copyright
Copyright © Australian Mathematical Society 1993

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]Daly, J. and Phillips, K., ‘On singular integrals, multipliers, H 1, and Fourier series-a local field phenomenon’, Math. Ann. 265 (1983), 181–219.CrossRefGoogle Scholar
[3]Garcia-Cuerva, J. and Rubio de Francia, J. L., Weighted norm inequalities and related topics (North-Holland, Amsterdam, 1985).Google Scholar
[4]Kurtz, D. S., ‘Littlewood-Paley operators on BMO’, Proc. Amer. Math. Soc. 99 (1987), 657–666.CrossRefGoogle Scholar
[5]Kurtz, D. S., ‘Singular integrals on BMO’, Proc. Centre Math. Anal. Austral. Nat. Univ. 16 (1987), 169–172.Google Scholar
[6]Taibleson, M., Fourier Analysis on Local Fields, Math. Notes (Princeton Univ. Press, Princeton, 1975).Google Scholar
[7]Wang, S., ‘Some properties of the Littlewood-Paley g-function’, Contemp. Math. 42 (1985), 191–202.CrossRefGoogle Scholar