Type and Order Convexity Ofmarcinkiewicz and Lorentz Spaces and Applications
نویسنده
چکیده
We consider order and type properties of Marcinkiewicz and Lorentz function spaces.We show that if 0 < p < 1, a p-normable quasi-Banach space is natural (i.e. embeds into a q-convex quasi-Banach lattice for some q > 0) if and only if it is finitely representable in the space Lp,∞. We also show in particular that the weak Lorentz space L1,∞ do not have type 1, while a non-normable Lorentz space L1,p has type 1. We present also criteria for upper r-estimate and r-convexity of Marcinkiewicz spaces. 2000 Mathematics Subject Classification. 46A16, 46B03, 46B20, 46E30.
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