loading page

Approach to the construction of the spaces $ S{D^p}[\R^{\infty}]$ for $1 \leq p \leq \infty$
  • Hemanta Kalita
Rajiv Gandhi University
Author Profile
Hemanta Kalita
Patkai Christian College (Autonomous), Dimapur
Author Profile


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.