分数次积分算子与分数次极大算子的有界性估计(英文)

THE BOUNDEDNESS ESTIMATES FOR FRACTIONAL INTEGRAL AND MAXIMAL OPERATORS

本文我们证明了如下结论: (1)分数次积分算子I_l与分数次极大算子M_l是K_(q1)^(α,p1)(1,ωα)到WK^(q2)^(α,p2)(1,ωβ)中的有界算子,其中q1=1,0<p1≤1,p1≤p2,0<β<1,α=β(n-l)/n,q2=n/(n-l),0<l<n且ωα(x)=|x|^(-α). (2)M_l是(L^p(|x|^(l(p-1))),Lp(|x|^(-l))型的(1<p<∞)且是弱(L^1,L^1(|x|^(-l)))型的.

In this paper we prove the following conclusions:(1)the fractional integral operator I_l and maximal operator M_l are bounded from K_(q1)^(α,p1)(1,ωα)to W K_(q2)^(α,p2)(1,ωβ), where q1=1,0<p1≤1,p1≤p2,0<β<1,α=β(n-l)/n,q2=n/(n-l),0<l<n andω_α(x)=|x|_(-α).(2)M_l is of strong type(L^p(|x|^(l(p-1))),L^p(|x|^(-l))(1<p<∞) and is of weak type(L^1,L^l(|x|(-l)).