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 2011 (vol 64 pp. 1329)
|Composition Operators Induced by Analytic Maps to the Polydisk|
We study properties of composition operators induced by symbols acting from the unit disk to the polydisk. This result will be involved in the investigation of weighted composition operators on the Hardy space on the unit disk and moreover be concerned with composition operators acting from the Bergman space to the Hardy space on the unit disk.
Keywords:composition operators, Hardy spaces, polydisk
Categories:47B33, 32A35, 30H10
3. CJM 2010 (vol 62 pp. 961)
|Multiplicative Isometries and Isometric Zero-Divisors|
For some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.
Keywords:Banach spaces of analytic functions, Hardy spaces, Bergman spaces, Bloch space, Dirichlet space, Dirichlet-type spaces, pointwise multipliers, coefficient multipliers, isometries, isometric zero-divisors
4. CJM 2009 (vol 62 pp. 439)
|On Hankel Forms of Higher Weights: The Case of Hardy Spaces|
In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by SundhÃ¤ll for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.
Keywords:Hankel forms, Schattenâvon Neumann classes, Bergman spaces, Hardy spaces, Besov spaces, transvectant, unitary representations, MÃ¶bius group
Categories:32A25, 32A35, 32A37, 47B35
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