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arXiv · 2112.12607

On the continuity of strongly singular Calderón-Zygmund-type operators on Hardy spaces

Claudio Vasconcelos·Tiago Picon
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Abstract

In this work, we establish results on the continuity of strongly singular Calderón-Zygmund operators of type $σ$ on Hardy spaces $H^p(\mathbb{R}^n)$ for $0<p\leq 1$ assuming a weaker $L^{s}-$type Hörmander condition on the kernel. Operators of this type include appropriated classes of pseudodifferential operators $OpS^{m}_{σ,b}(\mathbb{R}^n)$ and operators associated to standard $δ$-kernels of type $σ$ introduced by Álvarez and Milman. As application, we show that strongly singular Calderón-Zygmund operators are bounded from $H^{p}_{w}(\mathbb{R}^n)$ to $L^{p}_{w}(\mathbb{R}^n)$, where $w$ belongs to a special class of Muckenhoupt weight.

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Claudio Vasconcelos, Tiago Picon. 2022-05-05. On the continuity of strongly singular Calderón-Zygmund-type operators on Hardy spaces. https://arxiv.org/abs/2112.12607

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