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On extensions of inequalities of Kolmogoroff and others and some applications to almost periodic functions

Published online by Cambridge University Press:  18 May 2009

C. J. F. Upton
C. J. F. Upton
Affiliation:
University Of Melbourne, Victoria, Australia
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Let f(x) be a complex function of a real variable, defined over the whole real line, which possesses n derivatives (the nth at least almost everywhere) and is such that . Then, if k is any integer for which 0< k < n, Kolmogoroff's inequality may be written as

,

or, by putting ,

The constant K=K (k, n) known explicitly and is the best possible, i.e., there is a (real) function for which equality holds (see Bang [1]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 1 , March 1972 , pp. 1 - 16
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

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