Growth property and slowly increasing behaviour of singular solutions of linear partial differential equations in the complex domain

Consider a linear partial differential equation in Cd+1 P(z,partial derivative )u(z) = f(z), where u(z) and f(z) admit singularities on the surface {z(0) = 0}. We assume that \f(z)\ less than or equal to A\z(0)\(c) in Some sectorial region with respect to to. We can give an exponent gamma* >0 for each operator P(z,partial derivative) and show for those satisfying some conditions that if For All epsilon > 0 There ExistsC(epsilon) such that \u(z)\ less than or equal to C-z exp(epsilon \z(0)\(-gamma*)) in the sectorial region, then \u(z)\ less than or equal to C\z(0)\(c') for some constants c' and C.