n-球面上的Cesàro算子的带权强性求和

Strong Summability with Weights for Cesdro Operator on n- Sphere

设1<p≤2,0<q≤2,δ>(n-1)/p-(n/2),f∈Lp(Ωn),σNδ(f)(x)表示,f(x)在n-球面Ωn上的Cesaro平均.本文证明了 其中非负权系数ak满足 (A是绝对常数),这个结果加强了现有的结论.

Let 1<p≤2,0<q≤2,δ>-1)/p-(n/2),f(x)∈Lp(Ω), and let σNδ(f)(x) de- note Cesaro means of f(x) on n-sphere. It is proved that where the weight coefficients ak satisfy ak2≥0 and ( A is an absolute con- stant).