洛伦兹空间上的分布函数的极限性质

Limiting property of distribution function in Lorentz space

用一个新颖的方法证明以下等式:limα→0+α^(p)d_(f)(α)=limα→∞α^(p)d_(f)(α)=0其中f∈L^(p,q)(X,μ),并且有0<p<∞和0<q<∞。也证明函数α^(p)在某种意义下不能再提升。特别地,当q=∞时,以上等式是不一定成立的。

In this paper,we give a novel proof for the following equality limα→0+α^(p)d_(f)(α)=limα→∞α^(p)d_(f)(α)=0 for f∈L^(p,q)(X,μ)with 0<p<∞,and 0<q<∞.We also prove that the functionα^(p)can not be improved_(f)or some sense.When q=∞,the above equality does not hold.