On multilinear distorted multiplier estimate and its applications

Abstract

In this article, we investigate the multilinear distorted multiplier estimate (Coifman-Meyer type theorem) associated with the Schrödinger 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 the 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 $d=1,2$.

24pages. arXiv admin note: text overlap with arXiv:1303.4354 by other authors

References in corpus (2)

• The $L^p$ boundedness of wave operators for Schrödinger Operators with threshold singularities
• The $L^p$ boundedness of wave operators for Schrödinger operators with threshold singularities II. Even dimensional case