1. CJM 2014 (vol 66 pp. 1358)
|Sharp Localized Inequalities for Fourier Multipliers|
In the paper we study sharp localized $L^q\colon L^p$ estimates for Fourier multipliers resulting from modulation of the jumps of LÃ©vy processes. The proofs of these estimates rest on probabilistic methods and exploit related sharp bounds for differentially subordinated martingales, which are of independent interest. The lower bounds for the constants involve the analysis of laminates, a family of certain special probability measures on $2\times 2$ matrices. As an application, we obtain new sharp bounds for the real and imaginary parts of the Beurling-Ahlfors operator .
Keywords:Fourier multiplier, martingale, laminate
Categories:42B15, 60G44, 42B20
2. 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
3. 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
4. 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
5. 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