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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.
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참고문헌 (9)
참고문헌 신청
Abdallah Hakawati / 1998 / The Multiplier Algebra of Orlicz Spaces / An-Naha Univ.J.Res 12:1~6
J. Diestel / 1977 / Mathematical Surveys, 15 / Amer. Math. Soc
T. Jurlewicz / 1986 / Law of the Iterated Logarithm for Wiener Processes with Values in Orlicz Spaces / Probability and Mathematical Statistics 7:159~167
M.A. Kransnoselskii / 1961 / Convex Functions and Orlicz Spaces / P. Nororodhoff, Ltd
A. Lawniczak / 1982 / Gaussian Measures on Orlicz Spaces and Abstract Wiener Spaces / Lecture Notes in Math 939:81~97
J. Diestel / 1977 / Mathematical Surveys, 15 / Amer. Math. Soc
T. Jurlewicz / 1986 / Law of the Iterated Logarithm for Wiener Processes with Values in Orlicz Spaces / Probability and Mathematical Statistics 7:159~167
M.A. Kransnoselskii / 1961 / Convex Functions and Orlicz Spaces / P. Nororodhoff, Ltd
A. Lawniczak / 1982 / Gaussian Measures on Orlicz Spaces and Abstract Wiener Spaces / Lecture Notes in Math 939:81~97
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