Weighted Norm Inequalities for Weyl Multipliers and Hermite Pseudo-Multipliers

Abstract

In this thesis we deal with two problems in harmonic analysis. In the first problem we discuss weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier theorems on the Heisenberg group and also show in the context of a theorem of Weis on operator valued Fourier multipliers that the R-boundedness of the derivative of the multiplier is not necessary for the boundedness of the multiplier transform. In the second problem we deal with a variation of a theorem of Mauceri concerning the Lp bound-edness of operators Mwhich are known to be bounded on L2 .We obtain sufficient conditions on the kernel of the operaor Mso that it satisfies weighted Lp estimates. As an application we prove Lp boundedness of Hermite pseudo-multipliers.