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The Full T1 Theorem for Certain Triebel - Lizorkin Spaces

✍ Scribed by Kunchuan Wang

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
985 KB
Volume
197
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Previous authors have considered generalizations of the David‐Journé __T__1 theorem to the scale of Triebel ‐ Lizorkin spaces (IR^n^) under the __T__1 = 0 and T = 0 assumptions, where T is a (generalized) Calderon ‐ Zygmund operator. We prove boundedness on (IR^n^) under weaker assumptions on __T__1 and __T__1, which are related to the sharp __T__1, T BMO assumptions for in the David‐Journé theorem. In some cases we also show that our conditions are sharp. By similar techniques, we also obtain sharper conditions for “families of molecules” and “norming families” for these spaces.

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