  In this paper we establish weighted $L^{q}$-$L^{p}$-maximal regularity for
linear vector-valued parabolic initial-boundary value problems with
inhomogeneous boundary conditions of static type. The weights we consider are
power weights in time and in space, and yield flexibility in the optimal
regularity of the initial-boundary data and allow to avoid compatibility
conditions at the boundary. The novelty of the followed approach is the use of
weighted anisotropic mixed-norm Banach space-valued function spaces of Sobolev,
Bessel potential, Triebel-Lizorkin and Besov type, whose trace theory is also
subject of study.
