1. 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
2. CJM 2000 (vol 52 pp. 381)
||Hardy Space Estimate for the Product of Singular Integrals |
$H^p$ estimate for the multilinear operators which are finite sums
of pointwise products of singular integrals and fractional
integrals is given. An application to Sobolev space and some
examples are also given.
Keywords:$H^p$ space, multilinear operator, singular integral, fractional integration, Sobolev space
3. CJM 1997 (vol 49 pp. 520)
||Classical orthogonal polynomials as moments |
We show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous
$q$-ultraspherical polynomials and Al-Salam-Chihara polynomials, in
certain normalization, are moments of probability measures. We use
this fact to derive bilinear and multilinear generating functions for
some of these polynomials. We also comment on the corresponding formulas
for the Charlier, Hermite and Laguerre polynomials.
Keywords:Classical orthogonal polynomials, \ACP, continuous, $q$-ultraspherical polynomials, generating functions, multilinear, generating functions, transformation formulas, umbral calculus
Categories:33D45, 33D20, 33C45, 30E05