1. CJM 2012 (vol 65 pp. 510)
|Transference of vector-valued multipliers on weighted $L^p$-spaces|
We prove restriction and extension of multipliers between weighted Lebesgue spaces with two different weights, which belong to a class more general than periodic weights, and two different exponents of integrability which can be below one. We also develop some ad-hoc methods which apply to weights defined by the product of periodic weights with functions of power type. Our vector-valued approach allow us to extend results to transference of maximal multipliers and provide transference of Littlewood-Paley inequalities.
Keywords:Fourier multipliers, restriction theorems, weighted spaces
2. CJM 2012 (vol 65 pp. 299)
|On Multilinear Fourier Multipliers of Limited Smoothness|
In this paper, we prove certain $L^2$-estimate for multilinear Fourier multiplier operators with multipliers of limited smoothness. As a result, we extend the result of CalderÃ³n and Torchinsky in the linear theory to the multilinear case. The sharpness of our results and some related estimates in Hardy spaces are also discussed.
Keywords:multilinear Fourier multipliers, HÃ¶rmander multiplier theorem, Hardy spaces
3. CJM 2011 (vol 63 pp. 1161)
|Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group|
We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group $\varGamma$ and relative Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum $\varLambda\subseteq\varGamma$, the norm of the Hilbert transform and the Riesz projection on Schatten-von-Neumann classes with exponent a power of 2, and the norm of Toeplitz Schur multipliers on Schatten-von-Neumann classes with exponent less than 1.
Keywords:Fourier multiplier, Toeplitz Schur multiplier, lacunary set, unconditional approximation property, Hilbert transform, Riesz projection
Categories:47B49, 43A22, 43A46, 46B28
4. CJM 1998 (vol 50 pp. 897)
|Fourier multipliers for local hardy spaces on ChÃ©bli-TrimÃ¨che hypergroups |
In this paper we consider Fourier multipliers on local Hardy spaces $\qin$ $(0