The objective of this paper is to construct an extension of the class of Jones distribution Banach spaces $SD^p[\R^n], 1\le p\le \infty,$ which appeared in the book by Gill and Zachary \cite{TG} to $S{D^p}[\R^{\infty}]$ for $1\leq p \leq \infty.$ These spaces are separable Banach spaces, which contain the Schwartz distributions as continuous dense embedding. These spaces provide a Banach space structure for Henstock-Kurzweil integrable functions that is similar to the Lebesgue spaces for Lebesgue integrable functions.

In this article we discuss Sobolev spaces on canonical Banach spaces. The completeness of the Sobolev spaces is discussed in these settings. The Hilbert structure of the Sobolev spaces is also discussed. Finally, in application, we discuss the Fourier transform and its relevance for Sobolev spaces on canonical Banach spaces.