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arXiv · 2206.03724

Stable decomposition of homogeneous Mixed-norm Triebel-Lizorkin spaces

Morten Nielsen
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Abstract

We construct smooth localized orthonormal bases compatible with homogeneous mixed-norm Triebel-Lizorkin spaces in an anisotropic setting on $\bR^d$. The construction is based on tensor products of so-called univariate brushlet functions that are constructed using local trigonometric bases in the frequency domain. It is shown that the associated decomposition system form unconditional bases for the homogeneous mixed-norm Triebel-Lizorkin spaces. In the second part of the paper we study nonlinear $m$-term nonlinear approximation with the constructed basis in the mixed-norm setting, where the behaviour, in general, for $d\geq 2$, is shown to be fundamentally different from the unmixed case. However, Jackson and Bernstein inequalities for $m$-term approximation can still be derived.

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Morten Nielsen. 2022-06-08. Stable decomposition of homogeneous Mixed-norm Triebel-Lizorkin spaces. https://arxiv.org/abs/2206.03724

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