2024-03-29T05:18:57Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/694902022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116A maximal inequality associated to Schr\{o}dinger type equation.Cho, YonggeunLee, SanghyukShim, YongsunSchrÄodinger type equationmaximal operatorangular regularity410In this note, we consider a maximal operator supt2R ju(x; t)j = supt2R jeit(D)f(x)j, where u is the solution to the initial value problem ut = i(D)u, u(0) = f for a C2 function with some growth rate at in¯nity. We prove that the operator supt2R ju(x; t)j has a mapping property from a fractional Sobolev space H 1 4 with additional angular regularity to L2 loc.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69490info:doi/10.14943/83836https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69490/1/pre685.pdfHokkaido University Preprint Series in Mathematics6851102005engpublisher