. FA ] 1 9 Fe b 20 07 THE WEAK BANACH - SAKS PROPERTY OF THE SPACE
نویسندگان
چکیده
In this paper we show the weak Banach-Saks property of the Banach vector space (L p µ) m generated by m L p µ-spaces for 1 ≤ p < +∞, where m is any given natural number. When m = 1, this is the famous Banach-Saks-Szlenk theorem. By use of this property, we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of a vector space R m and vector-valued functions in a weakly compact subset of the space (L p µ) m for 1 ≤ p < +∞ and inequalities when these vector-valued functions are in a weakly* compact subset of the product space (L ∞ µ) m generated by m L ∞ µ-spaces.
منابع مشابه
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