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On multilinear distorted multiplier estimate and its applications
  • kailong yang
kailong yang
Institute of Applied Physics and Computational Mathematics
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Abstract

In this article, we investigate the multilinear distorted multiplier estimate (Coifman-Meyer type theorem) associated with the Schr\“{o}dinger operator $H=-\Delta + V$ in the framework of the corresponding distorted Fourier transform. Our result is the “distorted” analog of the multilinear Coifman-Meyer multiplier operator theorem in \cite{CM1}, which extends the bilinear estimates of Germain, Hani and Walsh’s in \cite{PZS} to multilinear case for all dimensions. As applications, we give the estimate of Leibniz’s law of integer order derivations for the multilinear distorted multiplier for the first time and we obtain small data scattering for a kind of generalized mass-critical NLS with good potential in low dimensions $d=1,2$.

Peer review status:UNDER REVIEW

03 Jul 2021Submitted to Mathematical Methods in the Applied Sciences
05 Jul 2021Assigned to Editor
05 Jul 2021Submission Checks Completed
14 Jul 2021Reviewer(s) Assigned
13 Sep 2021Review(s) Completed, Editorial Evaluation Pending