Lipschitz linearization of the maximal hyperbolic cross multiplier

Abstract

We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition and a lower bound on the linearizing function, we obtain $L^p({\mathbb{R}}^2)\to L^p({\mathbb{R}}^2)$ bounds for all $1<p<\infty$. We discuss various related results.

16 pages

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