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Journal of Fourier Analysis and Applications

, Volume 22, Issue 6, pp 1381–1415 | Cite as

Boundedness of Multilinear Pseudo-differential Operators on Modulation Spaces

  • Shahla Molahajloo
  • Kasso A. OkoudjouEmail author
  • Götz E. Pfander
Article

Abstract

Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the operators’ symbols. The flexibility and strength of the introduced methods is demonstrated by their application to the bilinear and trilinear Hilbert transform.

Keywords

Multilinear pseudo-differential operators Modulation spaces Bilinear Hilbert transform Trilinear Hilbert transform 

Mathematics Subject Classification

Primary 47G30 Secondary 35S99 42A45 42B15 42B35 

Notes

Acknowledgments

K.A. Okoudjou was partially supported by a RASA from the Graduate School of UMCP, the Alexander von Humboldt foundation, and by a grant from the Simons Foundation (\(\# 319197\) to Kasso Okoudjou). G.E. Pfander appreciates the hospitality of the mathematics departments at MIT and at the TU Munich. This project originated during a sabbatical at MIT and was completed during a visit of TU Munich as John von Neumann Visiting Professor. G.E. Pfander also appreciates funding from the German Science Foundation (DFG) within the project Sampling of Operators.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Shahla Molahajloo
    • 1
  • Kasso A. Okoudjou
    • 2
    Email author
  • Götz E. Pfander
    • 3
  1. 1.Department of MathematicsInstitute for Advanced Studies in Basic Sciences (IASBS)Gava zang, ZanjanIran
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA
  3. 3.School of Science and EngineeringJacobs UniversityBremenGermany

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