Weighted inequalities for multivariable dyadic paraproducs

2010/01/09 by Daewon Chung, Chung, Daewon
Mathematics · #42A35 #47B38 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:42A35 #msc:47B38

paper · pdf · doi:10.48550/arxiv.1001.1461

23 pages

arxiv created 2010/11/22 · arxiv updated 2010/11/23

Abstract

Using Wilson's Haar basis in \Rⁿ, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in \Rⁿ. We can then extend "trivially" Beznosova's Bellman function proof of the linear bound in L²(w) with respect to [w]_A2 for the 1-dimensional dyadic paraproduct. Here trivial means that each piece of the argument that had a Bellman function proof has an n-dimensional counterpart that holds with the same Bellman function. The lemma that allows for this painless extension we call the good Bellman function Lemma. Furthermore the argument allows to obtain dimensionless bounds in the anisotropic case.

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