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The Full T1 Theorem for Certain Triebel ‐ Lizorkin Spaces
Author(s) -
Wang Kunchuan
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19991970108
Subject(s) - mathematics , operator (biology) , pure mathematics , discrete mathematics , biochemistry , chemistry , repressor , transcription factor , gene
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.