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arXiv · 1709.04552

On the Calder\'{o}n-Zygmund structure of Petermichl's kernel. Weighted inequalities

Hugo Aimar·Ivana Gómez
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Abstract

We show that Petermichl's dyadic operator $\mathcal{P}$ (S. Petermichl (2000), Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol) is a Calder\'{o}n-Zygmund type operator on an adequate metric normal space of homogeneous type. As a consequence of a general result on spaces of homogeneous type, we get weighted boundedness of the maximal operator $\mathcal{P}^*$ of truncations of the singular integral. We show that dyadic $A_p$ weights are the good weights for the maximal operator $\mathcal{P}^*$ of the scale truncations of $\mathcal{P}$.

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Hugo Aimar, Ivana Gómez. 2017-09-13. On the Calder\'{o}n-Zygmund structure of Petermichl's kernel. Weighted inequalities. https://arxiv.org/abs/1709.04552

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