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A NOTE ON ANALOGUE OF WIENER SPACE WITH VALUES IN ORLICZ SPACE

PARK, YEON HEE

  • Received : 2015.10.23
  • Accepted : 2015.12.01
  • Published : 2015.12.25

Abstract

In this note we find the upper bound for ${\rho}(u^n,M)=\int_{0}^{T}\int_{0}^{{\mid}u(t){\mid}^n}p(s)dsdt$ and show that $F(y)=y^n$ is $m_{\phi}^M$-Bochner integrable on $C(\mathcal{O} _M)$ for $0{\leq}t{\leq}T$ when $\int_{\mathcal{O}_M}{\parallel}u_0{\parallel}_M^nd{\phi}(u_0)$ is finite.

Keywords

analogue of Wiener measure space;Orlicz space

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