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

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.