论文标题
希尔伯特（Hilbert）在邓克尔（Dunkl-Hardy）空间
Hilbert transform on the Dunkl-Hardy Spaces
论文作者
论文摘要
对于$ p> p_0 = \ frac {2λ} {2λ+1} $，带有$λ> 0 $，hardy space $h_λ^p（\ mathbb {r} _+^2）$与dunkl transform $ \ mathcal {f}_λ$ and dunkl the dunkl the there there there dunkl $ d $ n e r \ n o \ n p $ $ d_xf（x）= f'（x）+\fracλ{x} [f（x）-f（-f（-x）] $，是上半平面上的$ f = u+iv $的集合$λ$ -CAUCHY-RIEMANN方程：$ d_xu- \ partial_y v = 0 $，$ \ partial_y u +d_xv = 0 $，和$ \ sup \ limits_ {y> 0} \ int _ {\ int _ {\ mathbb {\ mathb {r}}}}} | f（x +iy）| [7]。然后在[11]中证明了真正的dunkl-hardy空间$h_λ^p（\ mathbb {r}）$ for $ \ frac {1} {1+γ_λ} <p \ leq1 $是同质的硬质空间。在本文中，我们将继续调查$λ$ -Hilbert在真正的dunkl-hardy空间上转换$h_λ^p（\ mathbb {r}）$ for $ \ frac {1} {1+γ_λ} <p \ p \ p \ p \ leq1 $，带有$γ_λ= 1/（4λ+2）$，并扩展了$λ$ -
For $p>p_0=\frac{2λ}{2λ+1}$ with $λ>0$, the Hardy space $H_λ^p(\mathbb{R}_+^2)$ associated with the Dunkl transform $\mathcal{F}_λ$ and the Dunkl operator $D$ on the real line $\mathbb{R}$, where $D_xf(x)=f'(x)+\fracλ{x}[f(x)-f(-x)]$, is the set of functions $F=u+iv$ on the upper half plane $\mathbb{R}^2_+=\left\{(x, y): x\in\mathbb{R}, y>0\right\}$, satisfying $λ$-Cauchy-Riemann equations: $ D_xu-\partial_y v=0$, $\partial_y u +D_xv=0$, and $\sup\limits_{y>0}\int_{\mathbb{R}}|F(x+iy)|^p|x|^{2λ}dx<\infty$ in [7]. Then it is proved in [11] that the real Dunkl-Hardy Spaces $H_λ^p(\mathbb{R})$ for $\frac{1}{1+γ_λ}<p\leq1$ are Homogeneous Hardy Spaces. In this paper, we will continue to investigate $λ$-Hilbert transform on the real Dunkl-Hardy Spaces $H_λ^p(\mathbb{R})$ for $\frac{1}{1+γ_λ}<p\leq1$ with $γ_λ=1/(4λ+2)$ and extend the results of $λ$-Hilbert transform in [7].
