Open Access
2011 Weighted inequalities for multivariable dyadic para-products
Daewon Chung
Publ. Mat. 55(2): 475-499 (2011).


Using Wilson's Haar basis in $\mathbb{R}^n$, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in $\mathbb{R}^n$. We can then extend "trivially'' Beznosova's Bellman function proof of the linear bound in $L^2(w)$ with respect to $[w]_{A_2}$ 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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Daewon Chung. "Weighted inequalities for multivariable dyadic para-products." Publ. Mat. 55 (2) 475 - 499, 2011.


Published: 2011
First available in Project Euclid: 22 June 2011

MathSciNet: MR2839452

Primary: 42B20
Secondary: 42B35

Keywords: anisotropic $A_p$-weights , multivariable dyadic paraproduct , Operator-weighted inequalities

Rights: Copyright © 2011 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.55 • No. 2 • 2011
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