Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE H1-STIELTJES INTEGRAL OF BANACH-VALUED FUNCTIONS

  • Yoon, Ju Han (Department of Mathematics Education Chungbuk University) ;
  • Park, Jae Myung (Department of Mathematics Chungnam National University) ;
  • Lee, Deok Ho (Department of Mathematics Education Kongju University)
  • Received : 2007.11.23
  • Published : 2008.03.31
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Abstract

In this paper, we define the $H_1$ - Stieltjes integral of Banach-valued functions which is a generalization of real-valued $H_1$ - Stieltjes integral and investigate some properties of $H_1$ - Stieltjes integral. Also we show that if $f:[a,b]{\rightarrow}X$ be a function with ${\dim}X\;<\;{\infty}$, then $f{\in}H_1LS([a,b],X,{\alpha})$ if and only if $f{\in}H_1S([a,b],X,{\alpha})$.

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