  Domain decomposition methods are a set of widely used tools for
parallelization of partial differential equation solvers. Convergence is well
studied for elliptic equations, but in the case of parabolic equations there
are hardly any results for general Lipschitz domains in two or more dimensions.
The aim of this work is therefore to construct a new framework for analyzing
nonoverlapping domain decomposition methods for the heat equation in a
space-time Lipschitz cylinder. The framework is based on a variational
formulation, inspired by recent studies of space-time finite elements using
Sobolev spaces with fractional time regularity. In this framework, the
time-dependent Steklov--Poincar\'e operators are introduced and their essential
properties are proven. We then derive the interface interpretations of the
Dirichlet--Neumann, Neumann--Neumann and Robin--Robin methods and show that
these methods are well defined. Finally, we prove convergence of the
Robin--Robin method and introduce a modified method with stronger convergence
properties.
