Endpoint estimates for the circular maximal function

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Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators (2019, background): “One of the authors [30] obtained most of the (left open) endpoint estimates for S̃ on the borderline for d ≥ 2 but there are still a few endpoint estimates of which validities are not settled yet.”
Bilinear restriction estimates for surfaces with curvatures of different signs (2005, methodology): “This type of estimate was used not only for the restriction problem but it also has applications for a variety of related problems (see [14, 16] and references therein, and also [4, 7, 8, 9]).”