Weak Type Bound for Oscillatory Singular Integrals

2016/06/01 by Lacey, Michael T.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.00375

Abstract

Let T _P f (x) = ∫ e ^{i P (y)} K (y) f (x-y) dy , where K (y) is a smooth Calderón-Zygmund kernel on \mathbb R ⁿ, and P be a polynomial. The maximal truncations of T_P satisfy the weak L ¹ inequality, our proof simplifying and extending the argument of Chanillo and Christ for the weak type bound for T_P.

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