  This article provides a functional analytical framework for boundary integral
equations of the heat equation in time-dependent domains. More specifically, we
consider a non-cylindrical domain in space-time that is the $C^2$-diffeomorphic
image of a cylinder, i.e., the tensor product of a time interval and a fixed
domain in space. On the non-cylindrical domain, we introduce Sobolev spaces,
trace lemmata and provide the mapping properties of the layer operators by
mimicking the proofs of [M. Costabel, Boundary integral operators for the heat
equation, Integral Equations and Operator Theory, 13(4):498-552, 1990]. Here it
is critical that the Neumann trace requires a correction term for the normal
velocity of the moving boundary. Therefore, one has to analyze the situation
carefully.
