The Besov class $B_{pq}^s$ is defined by ${ f : {
2^{|n|s}||W_n*f||_p
} _{ninmathbb{Z}}in ell^q(mathbb{Z}) }$. When $s=1$, $p=q
$, we know if $f in B_p$ if and only if
$int_mathbb{D}
|f^{(n)}(z)|^p(1-|z|^2)^{2pn-2}dv(z) <+infty$. It is shown in [5]
that $int_{mathbb{D}}|f^{'}(z)|^q K(z,z)^{1-q}dv(z)=
O(L(b(e^{-(q-p)^{-1}})))$ if $f in B_{L,p}$. In this paper we
will show that $f
in B_{L,p}$ if and only if
$sum_{n=0}^{infty}2^{nq}||W_n*f||_p^q =
O(L(b(e^{-(q-p)^{-1}})))$.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0620106-132718 |
| Date | 20 June 2006 |
| Creators | Yang, Hui-min |
| Contributors | none, none, Ngai-Ching Wong, Mark C. Ho |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620106-132718 |
| Rights | withheld, Copyright information available at source archive |
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