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I'm reading a paper used Sobolev space $H^s(\Omega)$ , I only know the definition of these space when $\Omega=R^n$ which used Fourier Transform, what if $\Omega$ is a bounded open set?

And I also want to know the bounded linear functional on this space look like?

Any suggestions are welcome!

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  • $\begingroup$ You may find this paper useful. It defines a fractional Sobolev space using the Laplacian operator and some functional calculus. $\endgroup$ – Berrick Caleb Fillmore Apr 25 '15 at 2:50
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Maybe you want to take a look to this paper: http://arxiv.org/abs/1104.4345

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