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BMO and singular integrals over local fields
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
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- Research Article
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- Copyright © Australian Mathematical Society 1993
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