Boundedness of Maximal Operators of Schr\'odinger Type with Complex Time
| Autor: | Bailey, Andrew D. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Rev. Mat. Iberoam. 29 (2013), no. 2 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4171/RMI/729 |
| Popis: | Results of P. Sj\"olin and F. Soria on the Schr\"odinger maximal operator with complex-valued time are improved by determining up to the endpoint the sharp $s \geq 0$ for which boundedness from the Sobolev space $H^s(\mathbb{R})$ into $L^2(\mathbb{R})$ occurs. Bounds are established for not only the Schr\"odinger maximal operator, but further for a general class of maximal operators corresponding to solution operators for certain dispersive PDEs. As a consequence of additional bounds on these maximal operators from $H^s(\mathbb{R})$ into $L^2([-1, 1])$, sharp results on the pointwise almost everywhere convergence of the solutions of these PDEs to their initial data are determined. Comment: 12 pages. One further minor correction. To appear in the Revista Matem\'atica Iberoamericana |
| Databáze: | arXiv |
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