In this note, we investigate the product Heisenberg group H<sup>n</sup>, where H<sup>n</sup>=H<sub>1</sub>×…×H<sub>1</sub> is the Cartesian product of the 3-d...In this note, we investigate the product Heisenberg group H<sup>n</sup>, where H<sup>n</sup>=H<sub>1</sub>×…×H<sub>1</sub> is the Cartesian product of the 3-dimensional Heisenberg group H<sub>1</sub>. Let （z, t）∈H<sup>n</sup>, （ζ, s）∈H<sup>n</sup> with z, ζ∈C<sup>n</sup>, s, t∈R<sup>n</sup>. The multiplication is given by （z, t）（ζ, s）=（z+ζ, τ）, where τ<sub>j</sub>=t<sub>j</sub>+s<sub>j</sub>-1/2 Imz<sub>j</sub>,1≤j≤n. Sometimes we shall also use coordinates （x, y, t）∈R<sup>2</sup>n×R<sup>n</sup>,展开更多
The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderon-Zygmund decomposition. Then the multiplier theorem in Lp(1 < p < ω ) is obtained. The special Hermite expansions...The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderon-Zygmund decomposition. Then the multiplier theorem in Lp(1 < p < ω ) is obtained. The special Hermite expansions in twisted Hardy space are also considered. As an application, the multipli-ers for a certain kind of Laguerre expansions are given in Lp space.展开更多
文摘In this note, we investigate the product Heisenberg group H<sup>n</sup>, where H<sup>n</sup>=H<sub>1</sub>×…×H<sub>1</sub> is the Cartesian product of the 3-dimensional Heisenberg group H<sub>1</sub>. Let （z, t）∈H<sup>n</sup>, （ζ, s）∈H<sup>n</sup> with z, ζ∈C<sup>n</sup>, s, t∈R<sup>n</sup>. The multiplication is given by （z, t）（ζ, s）=（z+ζ, τ）, where τ<sub>j</sub>=t<sub>j</sub>+s<sub>j</sub>-1/2 Imz<sub>j</sub>,1≤j≤n. Sometimes we shall also use coordinates （x, y, t）∈R<sup>2</sup>n×R<sup>n</sup>,
文摘The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderon-Zygmund decomposition. Then the multiplier theorem in Lp(1 < p < ω ) is obtained. The special Hermite expansions in twisted Hardy space are also considered. As an application, the multipli-ers for a certain kind of Laguerre expansions are given in Lp space.
