We characterize the boundedness and compactness of dyadic paraproducts on local dyadic fractional Sobolev spaces, Hs. We apply this result to establish the algebra property for Hs when s∈(21,1)
Nearby in the stack
and to deduce the boundedness and compactness of commutators with the Haar shift on
Hs
. Our conditions are stated in terms of new dyadic fractional
BMOs
and
CMOs
conditions involving the dyadic fractional Sobolev capacity, and our proof uses a new dyadic fractional version of the Carleson embedding theorem.
arXiv did not return neighbours for this paper. Try again in a bit.