Journal of the Korean Mathematical Society (대한수학회지)
- Volume 33 Issue 3
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- Pages.481-494
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
LOCAL GENERALIZED SOBOLEV SPACES
Abstract
We introduced the generalized Sobolev space $H_\omega^s$ in [4]. In this paper, we introduce the space $H_\omega^s(\Omega)$ of the generalized distributions in $H_\omega^s$ with compact supports in $\Omega$ and the local generalized Sobolev spaces $H_{\omega loc}^s(\Omega)$ of the generalized distributions on $\Omega$ which are locally in $H_\omega^s$ and study their properties.