论文标题
Lebesgue空间中Dunkl-Hausdorff操作员的界限
Boundedness of Dunkl-Hausdorff operator in Lebesgue spaces
论文作者
论文摘要
在本文中，$ l^p_v（\ r）$ - dunkl-hausdorff运算符$ \ displaystyle h _ _ {\ al，ϕ} f（x）= \ ent \ ent \ frac { | ϕ（t）|} {| t |^{2 \ al+2}} f \ lf（\ frac {x} {t} {t} \ rh）dt $ 已经进行了特征，并且对于某种类型的重量$ v $，已获得norm $ \ | h _ {\ al，ϕ} \ | _ {l^p_v（\ r）\ to l^p_v（\ r）} $的确切值。这涵盖了几个现有结果。还证明了两个维度的类似结果。
In this paper, the $L^p_v(\R)$-boundedness of the Dunkl-Hausdorff operator $\displaystyle H_{\al,ϕ} f(x)=\ent\frac{ |ϕ(t)|}{|t|^{2\al+2}}f\lf(\frac{x}{t}\rh) dt $ has been characterized and for a certain type of weight $v$, the precise value of the norm $\|H_{\al,ϕ}\|_{L^p_v(\R)\to L^p_v(\R)}$ has been obtained. This covers several of the existing results. Analogous results in two dimensions have also been proved.
