Posted by: Shuanglin Shao | June 14, 2010

On localization of the Schrodinger maximal function

I was interested in the almost everywhere pointwise convergence problem of the Schrödinger solution e^{it\Delta}f as time goes to zero since I was a graduate student. The question was raised by Carleson, and remains open in high dimensions. It is closely related to the boundedness of the Schrodinger maximal operator (local or global); in turn it is closely related to the interesting oscillatory integrals in harmonic analysis and Strichartz estimates in PDE. Recently I understood some of the problem and wrote down a note to re-construct the two dimensional proof. These results contained in this note are not new; in the note I explore them from a slightly different perspective.

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