  In this paper n-dimensional Sobolev type spaces $ E_{\alpha}^{s,p}(\R^n_+)$
$(\alpha\in \R^n,\;\;\alpha_1> -\frac{1}{2},...,\alpha_n>-\frac{1}{2}, s\in \R,
p\in [1,+\infty])$ are defined on $\R^n_+$ by using Fourier-Bessel transform.
Some properties including completeness and embedding results for these spaces
are obtained, Poincar\'{e}'s inequality and Reillich theorem are proved.
