Dyadic paraproducts are bounded and compact on local fractional Sobolev spaces H^s under new dyadic fractional BMO^s conditions, yielding the algebra property for s in (1/2,1) and commutator boundedness via a new fractional Carleson embedding theorem.
Sarason,Functions of vanishing mean oscillation, Trans
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Local dyadic fractional Sobolev spaces: paraproducts, commutators, and the algebra property
Dyadic paraproducts are bounded and compact on local fractional Sobolev spaces H^s under new dyadic fractional BMO^s conditions, yielding the algebra property for s in (1/2,1) and commutator boundedness via a new fractional Carleson embedding theorem.