Stat 210b Hwk #3 Solutions (due March 13)
نویسنده
چکیده
More generally, in the first claim we can replace the Lp(Q) norm with any norm || · || on F with the Riesz property, which is that |f | ≤ |g| (pointwise) implies ||f || ≤ ||g||. For the second claim, we can use any norm that has the Riesz property and for which the norm of the constant function f ≡ 1 is 1, which is clearly satisfied by Lp(Q) when Q is a probability measure. With these more general conditions, it follows immediately that H∞,B(ε,F) = H∞(ε/2,F)
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