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The Generalization of Paraproducts and the Full T1 Theorem for Sobolev and Triebel–Lizorkin Spaces

✍ Scribed by Kunchuan Wang

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 350 KB
Volume: 209
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5381

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✦ Synopsis

We study the boundedness of generalized Calderon᎐Zygmund operators acting ón Sobolev and, more generally, Triebel᎐Lizorkin spaces of arbitrary order of Ž ␥ . Ž ␥ . smoothness. We are able to relax the assumptions T x s 0 andror T * x s 0, which have been required in earlier results by other authors. To do this, we consider generalized paraproduct operators. We obtain the sharpness of our assumptions for some special cases. Using the same technique, we also obtain some sharper results for ''norming' ' and ''molecular'' families.

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