Linear bound for the dyadic paraproduct on weighted Lebesgue space L2(w)

By O. Beznosova. 2007

62 citations recorded by the source corpus.

The dyadic paraproduct is bounded in weighted Lebesgue spaces Lp(w) if and only if the weight w belongs to the Muckenhoupt class Apd. However, the sharp bounds on the norm of the dyadic paraproduct are not known even in the simplest L2(w) case. In this paper we prove that the bound on the norm of the dyadic paraproduct in the weighted Lebesgue space L2(w) depends linearly on the A2d characteristic of the weight w using Bellman function techniques and extrapolate this result to the Lp(w) case.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dc021ab37281e0d7e2259490d5a1493f27e11ec6

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A simple proof of the $A_2$ conjecture (2012, background): “• Beurling transform (Petermichl and Volberg [23], 2002); • Hilbert transform (Petermichl [21], 2007); • Riesz transform (Petermichl [22], 2008); • Dyadic paraproduct (Beznosova [2], 2008); • Haar shift (Lacey et al.”
Sharp A2 inequality for Haar shift operators (2009, methodology): “Recently, Beznosova [2], has proved the linear bound for discrete paraproduct operators, again using the Bellman function method.”
A Simple Proof of the A2 Conjecture (2013, background): “• Beurling transform (Petermichl and Volberg [23], 2002); • Hilbert transform (Petermichl [21], 2007); • Riesz transform (Petermichl [22], 2008); • Dyadic paraproduct (Beznosova [2], 2008); • Haar shift (Lacey et al.”
Sharp weighted estimates for classical operators (2010, methodology): “6 was first proved by Beznosova [2] using Bellman function techniques.”