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Multilinear And Multiparameter Pseudo-Differential Operators And Trudinger-Moser Inequalities, Lu Zhang

Wayne State University Dissertations

Pseudo-differential operators play important roles in harmonic analysis, several complex variables, partial differential equations and other branches of modern mathematics. We studied some types of multilinear and multiparameter Pseudo-differential operators. They include a class of trilinear Pseudo-differential operators, where the symbols are in the forms of products of Hormander symbols defined on lower dimensions, and we established the Holder type Lp estimate for these operators. They derive from the trilinear Coifman-Meyer type operators with flag singularities. And we also studied a class of bilinear bi-parameter Pseudo-differential operators, where the symbols are taken from the general Hormander class, and we studied …