Triebel-Lizorkin空间上的广义Abel平均

Generalized Abel means on Triebel Lizorkin spaces

对０＜ｐ≤１，得到了任意正阶δ＞０的广义Ａｂｅｌ平均Ｍδε（ｆ）在ＴｒｉｅｂｅｌＬｉｚｏｒｋｉｎ空间·Ｆα，ｑｐ（Ｒｎ）上的有界性结果‖Ｍδε（ｆ）‖·Ｆα，ｑｐ≤Ｃ‖ｆ‖·Ｆα，ｑｐ，由此得到ｌｉｍε→０＋‖Ｍδε（ｆ）－ｆ‖·Ｆα，ｑｐ＝０．

For 0<p≤1, the boundedness of generalized Abel means M δ ε(f) on Triebel Lizorkin spaces has been obtained: ‖M δ ε(f)‖ AF·U5 α,q p ≤C‖f‖ AF·U5 α,q p , this implies that lim ε→0 +‖M δ ε(f)-f‖ AF·U5 α,q p =0.