Stable decomposition of homogeneous Mixed-norm Triebel-Lizorkin spaces

M Nielsen*

*Kontaktforfatter

Publikation: Working paper/PreprintPreprint

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Abstrakt

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.
OriginalsprogEngelsk
StatusUdgivet - 8 jun. 2022

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