A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels
A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels
We give a complete characterisation of the spaces $\dot{B}^{\alpha}_{p,q}$ and $\dot{F}^{\alpha}_{p,q}$ by using a non-smooth kernel satisfying near minimal conditions. The tools used include a Stromberg-Torchinsky type estimate for certain maximal functions and the concept of a distribution of finite growth, inspired by Stein. Moreover, our exposition also makes essential …