Weighted inequalities for multivariable dyadic paraproducts
- Autores: Daewon Chung
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 55, Nº 2, 2011, págs. 475-499
- Idioma: inglés
- DOI: 10.5565/publmat_55211_10
- Enlaces
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Resumen
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 func- tion 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. Further- more the argument allows to obtain dimensionless bounds in the anisotropic case.
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