设球面平均函数为Mt(f)(x)=∫S^n-1f(x-ty′)dσ(y′),则当f∈L^p(R^n)是向径函数,n≥3,1≤P≤n/n-1时,lim↑t→0Mt(f)(x)=f(x)几乎处处成立。
Define spherical meansMt(f)(x)=∫S^n-1f(x-ty′)dσ(y′).Then lim↑t→0Mt(f)(x)=f(x) almost everywhere, provided radial function f∈L^p(R^n),n≥3,1≤P≤n/n-1.