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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
Abstract
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.
- 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
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