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In this paper we study singular integral operators which are hyper or weakover Lipschitz or Holder spaces and over weghted Sobolev spaces defined onunbounded domains in the standard $n$-D space $R^n$ for $n>0$. The$\pi$-operator in this case is one of the hyper integral operators which hasbeen studied extensively than other hyper singular integral operators. It willbe shown the control of singularity of such integral operators that are definedinterms of Cauchy generating kernels by working on weghted Sobolev spaces$W^{p,k}(\Omega,|x|^{\zeta+epsilon}dx)$ for some $\epsilon>0$ and $\zeta $ somepositive integer.

On Hyper Singular Integral Operators over Weighted Sobolev Spaces