An improved maximal inequality for 2D fractional order Schrödinger operators
Changxing Miao, Jianwei Yang, Jiqiang Zheng (2015)
Studia Mathematica
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The local maximal operator for the Schrödinger operators of order α > 1 is shown to be bounded from to L² for any s > 3/8. This improves the previous result of Sjölin on the regularity of solutions to fractional order Schrödinger equations. Our method is inspired by Bourgain’s argument in the case of α = 2. The extension from α = 2 to general α > 1 faces three essential obstacles: the lack of Lee’s reduction lemma, the absence of the algebraic structure of the symbol and the...