On the normal solvability of elliptic equations in the Holder space functions on plane

The uniformly elliptic equation
$$ Lw\equiv w_{\overline{z}}+q_1(z)w_z+q_2(z)\overline{w}_{\overline{z}}+a(z)w+b(z)\overline{w}=f(z) $$
with coefficients in the Holder space functions $C_\alpha$ on plane are considered. The equivalency following assertions is established: a) the operator $L: C_\alpha^1\to C_\alpha$ is $n$-normal; b) the a priori estimate
$$ ||w||_{1,\alpha}\leqslant M(||Lw||_\alpha+\max_{|z|\leqslant1}|w(z)|), $$
is valid; c) a corresponding limit equations has only the zero solution in $C^1_\alpha$.