Weigthed Norm Inequalities For Sublinear Operators

In this dissertation, the boundedness for a class of sublinear operators are mainly considered.In the first chapter, similar to Ap, we introduce the family of the power functions AP(w) with a power function w. We mainly prove that u Ap(w) is the necessary and sufficient condition for the strong type inequalityIn the second chapter, we give the (Lp(vp},Lq(uq}} boundedness for a class of multilinear operators T ,a,A1,A2 ....Ak and M a,A1,A2,...,AkIn the third chapter, we prove the following conclusions: (1) fractional integral operator It and fractional maximal operator Ml areIn the fourth chapter, we give vector-valued inequalities of maximal operators M, Mn and study the LP1 × LP2 ×....× Lpk(w) boundedness for rough operator...