THE H1-STIELTJES INTEGRAL OF BANACH-VALUED FUNCTIONS

Abstract

In this paper, we define the H1 -Stieltjes integral of Banach-valued functions which is a generalization of real-valued H1 Stieltjes integral and investigate some properties of H1 Stieltjes integral. Also we show that if f : [a, b] → X be a function with dim X < ∞, then f ∈ H1LS([a, b], X, α) if and only if f ∈ H1S([a, b], X, α).

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