Approach to the construction of the spaces $ S{D^p}[\mathbb{R}^{\infty}]$ for $1 \leq p \leq \infty$

Abstract

The objective of this paper is to construct an extension of the  class of Jones distribution Banach spaces $S{D^p}[\mathbb{R}^{n}], 1\leq p\leq \infty,$ which appeared in the book by Gill and Zachary \cite{TG} to  $S{D^p}[\mathbb{R}^{\infty}]$  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.