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Boundedness of multilinear commutators of generalized fractional integrals

✍ Scribed by Huixia Mo; Shanzhen Lu

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 180 KB
Volume: 281
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200510681

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✦ Synopsis

Abstract

Let L be the infinitesimal generator of an analytic semigroup on L^2^(ℝ^n^ ) with Gaussian kernel bound, and let L^–α /2^ be the fractional integral of L for 0 < α < n. Suppose that b = (b~1~, b~2~, …, b~m~ ) is a finite family of locally integral functions, then the multilinear commutator generated by b and L^–α /2^ is defined by

L^–α /2^~b~f = [b~m~ , …, [b~2~, [b~1~, L^–α /2^]], …, ] f,

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