An extrapolation of operator-valued dyadic paraproducts

Abstract

We consider the dyadic paraproducts πφ on 𝕋 associated with an ℳ-valued function φ. Here 𝕋 is the unit circle and ℳ is a tracial von Neumann algebra. We prove that their boundedness on Lp(𝕋, Lp(ℳ)) for some 1 < p < ∞ implies their boundedness on Lp(𝕋, Lp(ℳ)) for all 1 < p < ∞ provided that φ is in an operator-valued BMO space. We also consider a modified version of dyadic paraproducts and their boundedness on Lp(𝕋, Lp(ℳ)).

Locations

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