We consider the problem of characterising Besov-Lipshitz and Triebel-Lizorkin
spaces using kernels with limited smoothness and decay. This extends the work of H.-Q.
Bui et al in [4] and [5] from kernels in S to more general kernels, including the Poisson
kernel. We overcome the difficulty of defining the convolution of a general kernel with a
distribution by using the concept of a bounded distribution introduced by E. Stein [12].
The characterisations we obtain are valid for the full range of indices.
| Identifer | oai:union.ndltd.org:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/2854 |
| Date | January 2008 |
| Creators | Candy, Timothy Lars |
| Publisher | University of Canterbury. Mathematics and Statistics |
| Source Sets | University of Canterbury |
| Language | English |
| Detected Language | English |
| Type | Electronic thesis or dissertation, Text |
| Rights | Copyright Timothy Lars Candy, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
| Relation | NZCU |
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