【摘要】 研究非二倍测度下截口上的分数次积分Iαf(x)=∫Rn(1/d(x,y)n-α)f(y)dμ(y),这里0<α<n,d(x,y)为截口上的拟度量.证明了Iα是从Lp(Rn)到Lorentz空间Lq,∞(Rn)的有界算子,同时还证明了增长条件μ(S(x,r))≤Crn,x∈Rn,r>0是上述结论成立的必要条件.更多还原

【Abstract】 The fractional integral operators associated to the sections for non-doubling measures are considered,which is defined by Iαf(x)=∫Rn(1/d(x,y)n-α)f(y)dμ(y),where 0<α<n,d(x,y) is a quasi-metric associated to the sections.It is obtained that Iα is a bounded operator from Lp(Rn) into the Lorentz space Lq,∞(Rn).And also it is proved that the growing condition μ(S(X,r))≤Crn,x∈Rn,r>0 is a necessary condition for the result.更多还原