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In this paper the authors prove unique solvability of the initial-Dirichlet problem for the heat equation in a cylindrical domain with Lipschitz base, lateral data in      L p , p ⩾  2 {L^p},p \geqslant 2      , and zero initial values. A Poisson kernel for this problem is shown to exist with the property that its      L 2 {L^2}      -averages over parabolic rectangles are equivalent to      L 1 {L^1}      -averages over the same sets.

Estimates of caloric measure and the initial-Dirichlet problem for the heat equation in Lipschitz cylinders