LOCAL L^p ESTIMATE FOR THE SOLUTION OF $bar partial-NEUMANN$ PROBLEM OVER $D_t={(w,z):Rewleq frac{|z^m-tw|^2}{m}}$

Assume that a distribution u satisfies conditions:$[bar partial u = f,u bot H({D_t})]$ on domain $D_t,uin Dom(bar partial _0^*),bar partial u in bar partial _1^*;bar partial f=0,fbot H^{0,1}$. It is proved that $phi_1uinL_{beta +frac{1}{2m}-epsilon}^p$ if $phi _2finL_beta ^p$,where is the potential space defined in [14]; $phi _1,phi _2in C_c^infinity(U),phi _2=1$ on suppt phi_1;U is a neighbourhood of the origin; epsilon is a small positive number. This result contains a result of D.C. Chang (in [3]) by setting t = 0.