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Paraproducts via $$H^{\infty}$$-functional calculus. (English) Zbl 1277.42020
This paper is one of many devoted to harmonic analysis of singular “non-integral” operators that arise from the functional calculus of a rough differential operator $$L$$. It is a technical prelude to [D. Frey and P. C. Kunstmann, Math. Ann. 357, No. 1, 215–278 (2013; Zbl 1280.42006)], where the $$L^2$$-boundedness of such operators is characterized. Here, the author studies mapping properties of associated paraproducts $\Pi(f,b)=\int_0^\infty Q_t[(Q_t b)(A_tP_t f)]dt/t,$ where $$P_t$$ and $$Q_t$$ are approximations and resolutions of the identity associated with $$L$$, and $$A_t$$ is an additional spatial averaging, needed in the absence of pointwise bounds for $$P_t$$.

##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B30 $$H^p$$-spaces 42B35 Function spaces arising in harmonic analysis 47A60 Functional calculus for linear operators
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##### References:
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