分数次积分算子的双权弱型赋范不等式

Two-Weight Weak Type Norm Inequalities for Fractional Integral Operators

证明了若权函数(u,v)满足下列A_p型条件:对δ＞0及任意的方体Q, |Q|^(pα/n)‖u‖L(log L)^(2p-1+δ),Q(1/|Q|∫_Qv(x))-(p′/pdx)^(p/p′)≤K＜∞,则分数次积分算子I_α,0＜α＜n,是从L^p(v)到L^(p,∞)(u)的有界算子,1＜p＜∞．

We prove that if the weights （u, v） satisfy the following Ap-type condition： for some δ〉 0 and for all cubes Q, ｜Q｜^（pα/n）‖u‖L（log L）^（2p-1＋δ）,Q（1/｜Q｜∫Qv（x））-（p′/pdx）^（p/p′）≤K〈∞,, then the fractional integral Iα,0〈α〈n,is bounded from L^p（v）to L^（p,∞）（u）,1〈p〈∞.