A simple proof of the boundedness of Bourgain’s circular maximal operator

R. Manna

School of Mathematics, Harish-Chandra Research Institute, Allahabad 211019, India

Abstract: Given a set $E=(0, \infty)$, the circular maximal operator $\mathcal{M}$ associated with the parameter set $E$ is defined as the supremum of the circular means of a function when the radii of the circles are in $E$. Using stationary phase method, we give a simple proof of the $L^p$, $p>2$ boundedness of Bourgain's circular maximal operator.

Keywords and phrases: circular maximal operator, oscillatory integrals, Littlewood–Paley square function.

MSC: 42B25, 42B20

Received: 13.04.2015

Language: English

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