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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 sequenceof weak solution of Sobolev spaces are convergence strongly in HK-Sobolevspace. Also, we obtain that the Sobolev space through Bessel Potential isdensely contained in HK-Sobolev spaces. Finally we find sufficient conditionfor the solvability of the divergence equation $\nabla.F= f,$ for $f$ is anelement of the subspace $K{S^p}[\R_I^n]$ and $n \in \N$, in the SoboHK-Sobolevspace $WS^{k,p}[\R_I^n] $ with the help of Fourier transformation.

HK-Sobolev space $W{S^{k,p}}$ on $\mathbb{R}^\infty$ and Bessel Potential