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Norm inequalities involving derivatives

Published online by Cambridge University Press:  14 November 2011

W. D. Evans  and
A. Zettl
W. D. Evans
Affiliation:
Department of Pure Mathematics, University College, Cardiff
A. Zettl
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, De Kalb, Illinois, U.S.A.
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Synopisis

A new method for studying inequalities of the type ‖y(r)‖2<ε‖Sk−ry(k)‖2 + K(ε)‖S−ry‖2 and ‖y′‖2≦ Kp(S)‖Sy″‖ ‖S−1y‖ is presented here. With this new approach we obtain new and far reaching extensions of previously known inequalities of this sort as well as simpler proofs of the known cases. In addition we obtain an inequality of type ‖Sy′‖<ε‖(Sy′)′‖ + K(ε)‖y‖ for a general class of functions S. Also we give an elementary operator-theoretic proof of Everitt's characterization of the best constant as well as all cases of equality for

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 51 - 70
Copyright
Copyright © Royal Society of Edinburgh 1978

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