Weighted inequalities for singular integral operators on the half-line
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 $L^p$-maximal regularity of first order, second order and fractional order Cauchy problems to 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.