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

Assume that a distribution u satisfies conditions:$\\bar \partial u = f,u \bot H({D_t})\]$ on domain $D_t,u\in Dom(\bar \partial _0^*),\bar \partial u \in \bar \partial _1^*;\bar \partial f=0,f\bot H^{0,1}$. It is proved that $\phi_1u\inL_{\beta +\frac{1}{2m}-\epsilon}^p$ if $\phi _2f\inL_\beta ^p$,where is the potential space defined in 14]; $\phi _1,\phi _2\in C_c^\infinity(U),\phi _2=1$ 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.