  Our goal in this article is to construct HK-Sobolev spaces on $\R^\infty$
which contains Sobolev spaces as dense embedding. We discuss that the sequence
of weak solution of Sobolev spaces are convergence strongly in HK-Sobolev
space. Also, we obtain that the Sobolev space through Bessel Potential is
densely contained in HK-Sobolev spaces. Finally we find sufficient condition
for the solvability of the divergence equation $\nabla.F= f,$ for $f$ is an
element of the subspace $K{S^p}[\R_I^n]$ and $n \in \N$, in the SoboHK-Sobolev
space $WS^{k,p}[\R_I^n] $ with the help of Fourier transformation.
