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Extensions of theorems of Gagliardo and Marcus and Mizel to Orlicz spaces

Published online by Cambridge University Press:  17 April 2009

Grahame Hardy
Grahame Hardy
Affiliation:
Division of External Studies, University of Queensland, St Lucia, Queensland 4067, Australia.
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Abstract

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In 1958, Gagliardo showed that if u is a locally integrable function on a domain Ω satisfying the cone condition, with all weak derivatives belonging to the Lebesgue space Lp (Ω) (1 ≤ p < ∞), then u belongs to Lp (Ω) also. We extend this result to Orlicz spaces, and use it to extend a result of Marcus and Mizel on Nemitsky operators between Sobolev spaces to Orlicz-Sobolev spaces.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1981 , pp. 121 - 138
Copyright
Copyright © Australian Mathematical Society 1981

References

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