JournalsrmiVol. 29, No. 2pp. 531–546

Boundedness of maximal operators of Schrödinger type with complex time

  • Andrew D. Bailey

    Tessella, Abingdon, Oxfordshire, Great Britain
Boundedness of maximal operators  of Schrödinger type with complex time cover
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Abstract

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 s0s \geq 0 for which boundedness from the Sobolev space Hs(R)H^s(\mathbb{R}) into L2(R)L^2(\mathbb{R}) 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 Hs(R)H^s(\mathbb{R}) into L2([1,1])L^2([-1, 1]), 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

DOI 10.4171/RMI/729