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Journal of Fourier Analysis and Applications

, Volume 24, Issue 6, pp 1661–1680 | Cite as

Analytic Smoothing Effect for the Nonlinear Schrödinger Equations Without Square Integrability

  • Gaku HoshinoEmail author
  • Ryosuke Hyakuna
Article
  • 133 Downloads

Abstract

In this study we consider the Cauchy problem for the nonlinear Schrödinger equations with data which belong to \(L^p,\)\(1<p<2.\) In particular, we discuss analytic smoothing effect with data which satisfy exponentially decaying condition at spatial infinity in \(L^p,\)\(1<p<2.\) We construct solutions in the function space of analytic vectors for the Galilei generator and the analytic Hardy space with the phase modulation operator based on \(L^{p}\).

Keywords

Analytic smoothing effect Analytic Hardy space Nonlinear Schrödinger equations 

Mathematics Subject Classification

35Q55 

Notes

Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments and suggestions.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Waseda UniversityTokyoJapan
  2. 2.Osaka UniversityToyonakaJapan

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