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arXiv · 1608.03782

Wavelet transforms for homogeneous mixed-norm Triebel--Lizorkin spaces

A. G. Georgiadis·J. Johnsen·M. Nielsen
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Abstract

Homogeneous mixed-norm Triebel--Lizorkin spaces are introduced and studied with the use of a discrete wavelet transformation, the so-called $φ$-transform. This extends the classical $φ$-transform approach introduced by Frazier and Jawerth to the setting of mixed-norm spaces. Moreover, the theory of the $φ$-transform is enhanced through a precise definition of the synthesis operator, in terms of a Pettis integral, and a number of rigorous results for this operator. Especially its terms can always be summed in any order, without changing the resulting distribution.

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A. G. Georgiadis, J. Johnsen, M. Nielsen. 2017-03-29. Wavelet transforms for homogeneous mixed-norm Triebel--Lizorkin spaces. https://doi.org/10.1007/s00605-017-1036-z

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