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Variation Reducing Properties of Decreasing Rearrangements

Published online by Cambridge University Press:  20 November 2018

Kong-Ming Chong
Kong-Ming Chong*
Affiliation:
University of Malaya, Kuala Lumpur 22-11, Malaysia
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One well-established characteristic of the operation of decreasing rearrangement is its variation reducing property. A systematic study of this property has been made in considerable detail by G.F.D. Duff in [5] and [6]. He proved some inequalities related to the operation of rearrangement in decreasing order showing that the total variation of a sequence or an absolutely continuous function is in general diminished by such rearrangement. He also showed that the Lp norm of the difference sequence (or the derivative function) is diminished by this rearrangement operation unless the given sequence (or absolutely continuous function) is already monotonie (or equal to a monotonie function almost everywhere).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 330 - 336
Copyright
Copyright © Canadian Mathematical Society 1975

References

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