Relations between Function Spaces
نویسنده
چکیده
With this norm, K(W) is a Banach space and even a Banach lattice, i.e., a vector lattice with the property that \g\ ^/, fEk(W) for a measurable g implies gGA(JF) and ||g|| á||/||. Condition (3) ensures [l, Theorem 5] that the norm (4) is continuous with respect to monotone limits. One obtains examples of such functions W as follows. Let (S, B, p.) be a measure space with measure p, which we shall in this paper assume nonatomic. If $o(w) is a positive increasing concave function of w = 0 with i>o(0+)=0, then one sees that W(e) =$0(pe) satisfies (1), (2), (3). An Orlicz space ¿$(5) is defined by an increasing convex function (w), w = 0 with 3>(0+)=0 and <3?'(m)—>oo, and by a measure space (S, B, p). We have/GP* if
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A new class of function spaces on domains of R^d and its relations to classical function spaces
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