Rearrangement-Invariant Spaces of Functions on LCA Groups
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 ...
متن کاملThe Level Function in Rearrangement Invariant Spaces
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.
متن کاملOn a Metric on Translation Invariant Spaces
In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.
متن کاملShift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1998
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3266