Reseach on multilinear harmonic analysis and its applications

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As an example of multilinear operators we studied multilinear pseudo-differential operators. In particular we got a condition of the symbol of multilinear pseudo-differential operators defined on products of a Hilbert space, which belong to the Schatten-von Neumann class. Moreover we provided the wavelet characterization of the weighted Herz spaces. Moreover we proved the Sobolev-Lieb-Thirring inequality with respect to the Bessel potentials by means of the wavelet characterization of weighted Lp spaces.