Wavelet transforms for homogeneous mixed-norm Triebel–Lizorkin spaces
By Athanasios G. Georgiadis, Jon Johnsen, Morten Nielsen. 2016
74 citations recorded by the source corpus.
Homogeneous mixed-norm Triebel–Lizorkin spaces are introduced and studied with the use of a discrete wavelet transformation, the so-called $$\varphi $$φ-transform. This extends the classical $$\varphi $$φ-transform approach introduced by Frazier and Jawerth to the setting of mixed-norm spaces. Moreover, the theory of the $$\varphi $$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.
Subfields: Applied Mathematics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c37fe99541d0099aa34db86556507fb14527c522
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In Applied Mathematics
- Jarod Hart
- Xinfeng Wu
- Rodolfo H. Torres
- Loukas Grafakos
- Dachun Yang
- Kabe Moen
- 'Arp'ad B'enyi
- Long Huang
In Statistics and Probability
Citations in the corpus
- Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces (2017, methodology): “For LL spaces with p, q > 1, this was carried out in [57] while for general Triebel–Lizorkin spaces based on LL it was done in the work [33] already mentioned in Section 2.”