The K-functional for rearrangement invariant spaces
نویسندگان
چکیده
منابع مشابه
Subspaces of Rearrangement-invariant Spaces
We prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y. For example we show that if Y is an r. i. space on [0, oo) which is/7-convex for some/? > 2 and has nontrivial concavity then any Banach lattice X which is r-convex for some r > 2 and embeds into Y must embed as a sublattice. Similar conclusions can be drawn under a variety of hypotheses on Y; if ...
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An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.
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The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 ^ V ̂ 2, p~ + q= 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p~ι9 it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to ςr such that the Fourier transform is a bounded linear operator from X...
متن کاملEmbeddings of Rearrangement Invariant Spaces That Are Not Strictly Singular
We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L1 ((0; 1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space L with (x) = exp(x 2) ? 1. In this paper we ask the following question. Given a rearrangement invariant space E on 0; 1], when ...
متن کاملEmbeddings of rearrangement invariant spaces that are not strictly singular
We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L1([0, 1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space LΦ with Φ(x) = exp(x 2) − 1. In this paper we ask the following question. Given a rearrangement invariant space E on [0, 1], whe...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1979
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-64-2-175-190