Weighted inequalities for singular integral operators on the half-line

2014/10/10 by Chill, Ralph, Krol, Sebastian · 1 citation
#34G10 #46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 42B20 #Secondary 47D06

paper · doi:10.48550/arxiv.1410.3457

Abstract

We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of the operators satisfy relaxed Dini conditions. We apply the weighted estimates to extrapolation of maximal L^p regularity of first order, second order and fractional order Cauchy problems into weighted rearrangement invariant Banach function spaces. In particular, we provide extensions, as well as a unification of recent results due to Auscher and Axelsson, and Chill and Fiorenza.

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• An A₂ Theorem for One-Sided Calderón-Zygmund Operators

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