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Cauchy Integral of Calderón on the Graphs of Functions with BMO Derivatives

Published online by Cambridge University Press:  20 November 2018

Kôzô Yabuta
Kôzô Yabuta*
Affiliation:
Department of Mathematics, Ibaraki University, Mito, Ibaraki 310, Japan
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Abstract

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We first note that each graph (x,A(x)) of a function A(x) with BMO derivative is a chord-arc curve. Using this, Muckenhoupt's Ap theory, and the theory of Calderón-Zygmund operators, we shall derive weighted norm inequalities for the Cauchy integral on such graphs from a recent theorem of G. David on the L2-boundedness of Cauchy integral on almost-lipschitzian curves.

Keywords

42B20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 495 - 500
Copyright
Copyright © Canadian Mathematical Society 1985

References

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