  We consider the Dirichlet problem in a wedge for parabolic equation whose
coefficients are measurable function of t. We obtain coercive estimates in
weighted $L_{p,q}$-spaces. The concept of "critical exponent" introduced in the
paper plays here the crucial role. Various important properties of the critical
exponent are proved. We give applications to the Dirichlet problem for linear
and quasi-linear non-divergence parabolic equations with discontinuous in time
coefficients in cylinders $\Omega\times(0,T)$, where $\Omega$ is a bounded
domain with an edge or with a conical point.
