Weighted Weak Type Inequalities For Potential Type Operators

For a non-negative,locally integrable functionΦ on R~n,the potential typeoperators associated toΦis defined byWe assume that the kernelΦsatisfies the following weak growth condition:thereexist constantsδ,c,0≤ε<1 with the property that for all k∈Z,and (?)(t)／t~n→0,as t→∞．whereThe main results are the following:(i)Letδ>0,for any weightω,we have(ii)Given 11 and any cube Q,then the potential type operators T_Φsatisfies the following two-weight weak type(p,q)inequality,...