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Hardy Inequalities with Mixed Norms

Published online by Cambridge University Press:  20 November 2018

J. Scott Bradley
J. Scott Bradley*
Affiliation:
McMaster University, Hamilton, Ontario, Canada
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We give a necessary and sufficient condition on weight functions u and v such that for l≤p≤q≤∞ there exists a constant C for which

A corresponding dual result is also given. This extends a result of B. Muckenhoupt which appeared in Studia Math., 34 (1972).

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 405 - 408
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Hardy, G. H., Note on a theorem of Hilbert, Math. Z. 6 (1920), 314-317.Google Scholar
2. Hardy, G. H., Notes on some points in the integral calculus LX, Messenger of Mathematics, 54 (1925), 150-156.Google Scholar
3. Muckenhoupt, B., Hardy's inequality with weights, Studia Math., 34 (1972), 31-38.Google Scholar
4. Zygmund, A., Trigometric Series, Volume I, Second Edition, Cambridge University Press, 1959.Google Scholar