1. CMB Online first
||Embedding theorem for inhomogeneous Besov and Triebel-Lizorkin spaces on RD-spaces|
In this article we prove the embedding theorem for inhomogeneous
Besov and Triebel-Lizorkin spaces on RD-spaces.
The crucial idea is to use the geometric density condition
on the measure.
Keywords:spaces of homogeneous type, test function space, distributions, CalderÃ³n reproducing formula, Besov and Triebel-Lizorkin spaces, embedding
Categories:42B25, 46F05, 46E35
2. CMB 2008 (vol 51 pp. 570)
||Amsterdam Properties of $C_p(X)$ Imply Discreteness of $X$ |
We prove, among other things, that if $C_p(X)$ is
subcompact in the sense of de Groot, then the space $X$ is
discrete. This generalizes a series of previous results on
completeness properties of function spaces.
Keywords:regular filterbase, subcompact space, function space, discrete space
Categories:54B10, 54C05, 54D30
3. CMB 1999 (vol 42 pp. 321)
||Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces |
We shall study some connection between averaging operators and
martingale inequalities in rearrangement invariant function spaces.
In Section~2 the equivalence between Shimogaki's theorem and some
martingale inequalities will be established, and in Section~3 the
equivalence between Boyd's theorem and martingale inequalities with
change of probability measure will be established.
Keywords:martingale inequalities, rearrangement invariant function spaces
Categories:60G44, 60G46, 46E30