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
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
the constants involve the analysis of laminates, a family of
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|
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
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)