Abstract
We present weighted Sobolev spaces \(\widetilde{\mathfrak {H}}_{p, \theta }^{\gamma }(S, T)\) and prove a trace theorem for the spaces. As an application, we discuss non-zero boundary value problems for parabolic equations. The weighted parabolic Sobolev spaces we consider are designed, in particular, for the regularity theory of stochastic partial differential equations on bounded domains.
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