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arXiv · 1507.08114

On the consequences of a Mihlin-Hörmander functional calculus: maximal and square function estimates

Błażej Wróbel
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Abstract

We prove that the existence of a Mihlin-Hörmander 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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Błażej Wróbel. 2015-07-29. On the consequences of a Mihlin-Hörmander functional calculus: maximal and square function estimates. https://arxiv.org/abs/1507.08114

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