Invariant weighted algebras $L_p^w(G)$

Details Invariant weighted algebras $L_p^w(G)$ Invariant weighted algebras $L_p^w(G)$

2007-07-02

arxiv.org/abs/0707.0009v2

Mat. Zametki 84, no. 4, pp. 567-576 (2008)

Mathematics

Functional Analysis

Submitted to Mat. Zametki. 12 pages

Scientific paper

The paper deals with weighted spaces $L_p^w(G)$ on a locally compact group G. If w is a positive measurable function on G then we define the space $L_p^w(G)$, $p\ge1$, as $L_p^w(G)=\{f:fw\in L_p(G)\}$. We consider weights such that these weighted spaces are algebras with respect to usual convolution. It is shown that for p>1 such weights exists on any sigma-compact group. We prove also a criterion known earlier in special cases: $L_1^w(G)$ is an algebra if and only if w is submultiplicative. It is proved that invariant algebras $L_p^w(G)$, $p>1$, have approximate units of standard form, but this may not be true for a non-invariant algebra.

Affiliated with

Also associated with

No associations

Rating

Invariant weighted algebras $L_p^w(G)$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Invariant weighted algebras $L_p^w(G)$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariant weighted algebras $L_p^w(G)$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-692112