Abstract
In this paper we present a brief survey on Haar multipliers, dyadic paraproducts, and recent results on their applications to deduce scalar and vector valued weighted inequalities. We present a new proof of the boundedness of a Haar multiplier in Lp(ℝ). The proof is based on a stopping time argument suggested by P. W. Jones for the case p = 2, that it is adapted to the case 1 < p < ∞ using an new version of Cotlar’s Lemma for Lp. We then prove some weighted inequalities for simple dyadic operators.
Research supported by EPSCR GR/110024
Research supported by EPSCR Visiting Fellowship GR/16066
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Katz, N.H., Pereyra, M.C. (1999). Haar multipliers, paraproducts, and weighted inequalities. In: Bray, W.O., Stanojević, Č.V. (eds) Analysis of Divergence. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2236-1_11
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DOI: https://doi.org/10.1007/978-1-4612-2236-1_11
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