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math.AP2016★ 8 cited
On local smoothing problems and Stein's maximal spherical means
Changxing Miao, Jianwei Yang, Jiqiang Zheng
It is proved that the local smoothing conjecture for wave equations implies certain improvements on Stein's analytic family of maximal spherical means. Some related problems are al…
math.AP2016★ 2 cited
Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces
Changxing Miao, Christopher D. Sogge, Yakun Xi +1
We obtain an improvement of the bilinear estimates of Burq, Gérard and Tzvetkov in the spirit of the refined Kakeya-Nikodym estimates of Blair and the second author. We do this by…