Sampling Multipliers and the Poisson Summation Formula.
Schauder decompositions and multiplier theorems
We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.
Singular integral operators with complex homogeneity
Some remarks on a theorem of S.M. Lozinski concerning linear process of approximation of periodic functions
Some singular measures on the circle which improve spaces
Spectral decompositions and harmonic analysis on UMD spaces
We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X.
Stability and Convergence Rates in Lp for Certain Difference Schemes.