On a solutions of one class of almost hypoelliptic equations

We prove, that if $P(D)=P(D_1,D_2)=\sum_{\alpha}\gamma_{\alpha} D_1^{\alpha_1}D_2^{\alpha_2}$ is an almost hypoelliptic regular operator, then for enough small $\delta>0$ all the solutions of the equation $P(D)u = 0$ from $L_{2,\delta} (R^2)$ are entire analytical functions.