Existence of a bounded Sobolev extension operator E from W^{p,1}(B, P) to W^{p,1}(ℓ², P) is proved for the unit ball B and any non-trivial centered Gaussian P, solving an open problem.
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Smooth functions are dense in Sobolev spaces over arbitrary open sets in ℓ², proving the infinite-dimensional H=W theorem.
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Extension of Sobolev functions on balls in infinite dimensions
Existence of a bounded Sobolev extension operator E from W^{p,1}(B, P) to W^{p,1}(ℓ², P) is proved for the unit ball B and any non-trivial centered Gaussian P, solving an open problem.
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"$H=W$" in infinite dimensions
Smooth functions are dense in Sobolev spaces over arbitrary open sets in ℓ², proving the infinite-dimensional H=W theorem.