向径函数的球面平均及其点态收敛性

Spherical means of radial function and its pointwise convergence

设球面平均函数为Mt(f)(x)=∫Sn-1f(x-ty′)dσ(y′),则当f∈Lp(Rn)是向径函数,n≥3,1<p≤n/(n-1)时,limt→0Mt(f)(x)=f(x)几乎处处成立.

Define spherical means Mt（f）（x）=∫s^n-1f（x-ty′）dσ（y′）.It is proved thatlim（t→0）Mt（f）（x）=f（x） holds almost everywhere,provided there is radial function f∈L^p（R^n）,n≥3,1〈p≤n/（n-1）.