Weighted Norm Inequalities for Maximally Modulated Singular Integral Operators
نویسندگان
چکیده
We present a framework that yields a variety of weighted and vector-valued estimates for maximally modulated Calderón-Zygmund singular (and maximal singular) integrals from a single a priori weak type unweighted estimate for the maximal modulations of such operators. We discuss two approaches, one based on the good-λ method of Coifman and Fefferman [CF] and an alternative method employing the sharp maximal operator. As an application we obtain new weighted and vector-valued inequalities for the Carleson operator and also for a related maximally modulated operator with quadratic phase studied by M. Lacey. We obtain that these operators are controlled by a natural maximal function associated with the Orlicz space L(logL)(log log logL). This control is in the sense of a good-λ inequality and yields strong and weak type estimates as well as vector-valued and weighted estimates for the operators in question.
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