We prove that the existence of a Mihlin-H\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The considered multiplier functions are finitely smooth and satisfy an integral condition at infinity. In particular multipliers of compact support are admitted.
Wrobel, B. (2015). On the consequences of a Mihlin-Hörmander functional calculus: maximal and square function estimates [Altro].
On the consequences of a Mihlin-Hörmander functional calculus: maximal and square function estimates
WROBEL, BLAZEJ JANPrimo
2015
Abstract
We prove that the existence of a Mihlin-H\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The considered multiplier functions are finitely smooth and satisfy an integral condition at infinity. In particular multipliers of compact support are admitted.
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