Geodesic
A simple proof of the boundedness of Bourgain’s circular maximal operator
Eurasian mathematical journal, Tome 6 (2015) no. 3, pp. 45-53

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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. 
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     title = {A simple proof of the boundedness of {Bourgain{\textquoteright}s} circular maximal operator},
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R. Manna. A simple proof of the boundedness of Bourgain’s circular maximal operator. Eurasian mathematical journal, Tome 6 (2015) no. 3, pp. 45-53. http://geodesic.mathdoc.fr/item/EMJ_2015_6_3_a3/