A study of Besov-Lipschitz and Triebel-Lizorkin spaces using non-smooth kernels
Degree GrantorUniversity of Canterbury
Degree NameMaster of Science
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  and  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 . The characterisations we obtain are valid for the full range of indices.