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arXiv · 2210.13130

A note on continuity of strongly singular Calder\'on-Zygmund operators in Hardy-Morrey spaces

Marcelo de Almeida·Tiago Picon·Claudio Vasconcelos
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Abstract

In this note we address the continuity of strongly singular Calder\'on-Zygmund operators on Hardy-Morrey spaces $\mathcal{HM}_{q}^{\lambda}(\mathbb{R}^n)$, assuming weaker integral conditions on the associated kernel. Important examples that falls into this scope are pseudodifferential operators on the H\"ormander classes $OpS^{m}_{\sigma,\mu}(\mathbb{R}^n)$ with $0<\sigma \leq 1$, $0 \leq \mu <1$, $\mu \leq \sigma$ and $m\leq -n(1-\sigma)/2$.

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Marcelo de Almeida, Tiago Picon, Claudio Vasconcelos. 2022-10-24. A note on continuity of strongly singular Calder\'on-Zygmund operators in Hardy-Morrey spaces. https://arxiv.org/abs/2210.13130

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