Dyadic fractional Sobolev spaces satisfy the expected embeddings and form an algebra under pointwise multiplication for sufficiently high regularity, with explicit counterexamples showing the algebra property fails at low regularity.
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Dyadic fractional Sobolev spaces: Embeddings and algebra property
Dyadic fractional Sobolev spaces satisfy the expected embeddings and form an algebra under pointwise multiplication for sufficiently high regularity, with explicit counterexamples showing the algebra property fails at low regularity.