J Austral Math Soc Ser A 54 pp321--333, 1993.

BMO and Singular Integrals over Local Fields

James E. Daly and Douglas S. Kurtz

Abstract

This paper is concerned with the behaviour of certain principle-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 is these spaces. Direct, constructive proofs of the eostence and boundedness of the altered operators under certain smoothness conditions on the kernel are given.

1991 AMS Subject Classification: 43A70, 42B20, 42B30

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Authors

James E. Daly

Department of Mathematics, University of Colorado, Colorado Springs, Colorado, 80933, USA.

Douglas S. Kurtz

Department of Mathematical Science, New Mexico State University, Las Cruces, New Mexico 88003, USA.