Timeline for Anisotropic Calderon-Zygmund decomposition
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 14, 2022 at 18:12 | comment | added | Giorgio Metafune | Sure, let me know. I forgot to mention the classical references Coifman-Weis and Christ....but you surely know them. | |
| Sep 14, 2022 at 12:31 | comment | added | Adi | Thanks a lot for the references, please give me a few days to see how helpful this version is and/or do I need more properties for my needs. | |
| Sep 14, 2022 at 7:16 | comment | added | Giorgio Metafune | I have in mind: P. Auscher "Real harmonic Analysis" (you find it free online press.anu.edu.au/publications/real-harmonic-analysis), Theorem 2.3.4. Chapter 2 deals with different coverings with or without the doubling property. Also the habilitation thesis by H. Koch math.uni-bonn.de/people/koch/public.html is very connected (see lemma 2.24 and proposition 2.2.7 for a CZ decomposition in this setting). | |
| Sep 14, 2022 at 5:22 | comment | added | Adi | Could you please let me know the reference for homogenous spaces and the theorem you are referring to so that i read it carefully first before replying to your comment. | |
| Sep 13, 2022 at 21:00 | comment | added | Giorgio Metafune | That is strange. Don't you have the same problem with dyadic cubes? Usually you don't know at which scale they are selected nor which centers. | |
| Sep 13, 2022 at 20:52 | comment | added | Adi | Unfortunately that isn't enough for my needs because that result is a bit of an existential one. In the sense, there exists a covering with CZ type properties, but the problem is that i don't know which balls are at which scale nor do i have any effective estimates on their locations. | |
| Sep 13, 2022 at 19:58 | comment | added | Giorgio Metafune | As an alternative, you could use Whitney balls which work well in homogenuous spaces and get somewhat weaker results for every $p$. Maybe they suffice. | |
| Sep 13, 2022 at 19:34 | comment | added | Adi | When k and h are integers, then the CZ theory works. In other cases, the subdivision will produce cylinders that could go over or stay below the previous generation. So I'm trying to understand how to subdivide in t direction when p isn't an integer or rational number. | |
| Sep 13, 2022 at 17:15 | comment | added | Giorgio Metafune | Just a simple remark, without having checked the details. If you subdivide into $k$ parts in $x$ and $h$ parts in $t$ you should get any $p=(\log k)/(\log h)$ with $k,h \geq 2$ integers (the case $k=2, h=4$ gives parabolic cylinders). Is this true? | |
| Sep 13, 2022 at 15:28 | history | edited | YCor | CC BY-SA 4.0 |
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| Sep 13, 2022 at 14:51 | history | asked | Adi | CC BY-SA 4.0 |