Results of P. Sjölin and F. Soria on the Schrödinger maximal operator with complex-valued time are improved by determining up to the endpoint the sharp for which boundedness from the Sobolev space into occurs. Bounds are established for not only the Schrödinger 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 into , sharp results on the pointwise almost everywhere convergence of the solutions of these PDEs to their initial data are determined.
Cite this article
Andrew D. Bailey, Boundedness of maximal operators of Schrödinger type with complex time. Rev. Mat. Iberoam. 29 (2013), no. 2, pp. 531–546