Weighted Norm Inequalities for Weyl Multipliers and Hermite Pseudo-Multipliers
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.
- Mathematics (MA) 
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