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arXiv · 1502.06836

A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels

Huy-Qui Bui·Timothy Candy
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Abstract

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 use of a number of refinements of the well-known Calderon reproducing formula. The results are then applied to obtain the characterisation of these spaces via a fractional derivative of the Poisson kernel.

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Huy-Qui Bui, Timothy Candy. 2015-02-24. A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels. https://arxiv.org/abs/1502.06836

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