2015/06/23 by Yong Ding, Ding, Yong, Xudong Lai +1
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #math.CA
paper · pdf · doi:10.48550/arxiv.1506.06956
Some misprints and the reference [6] of published version are corrected. Published in J.Geom.Anal(2015)
arxiv created 2015/09/16 · arxiv updated 2015/09/17
Let K be the Calderón-Zygmund convolution kernel on ℝd (d≥2). Define the commutator associated with K and a∈ L^∞(ℝd) by Taf(x)=p.v. ∫ K(x-y)mx,ya⋅ f(y)dy. Recently, Grafakos and Honz'ık [5] proved that Ta is of weak type (1,1) for d=2. In this paper, we show that Ta is also weighted weak type (1,1) with the weight |x|α (-2<α<0) for d=2. Moreover, we prove that Ta is bounded on weighted Lp(ℝd) (1<p<∞) for all d≥2.