Abstract
In this work, we establish results on the continuity of strongly singular Calderón–Zygmund operators of type \(\sigma \) on Hardy spaces \(H^p(\mathbb R^n)\) for \(0<p\le 1\) assuming a weaker \(L^{s}\)-type Hörmander condition on the kernel. Operators of this type include appropriate classes of pseudodifferential operators \(OpS^{m}_{\sigma ,b}(\mathbb R^n)\) and operators associated to standard \(\delta \)-kernels of type \(\sigma \) 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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Notes
The notation \(f \lesssim g \) means that there exists a constant \(C>0\) such that \(f(x)\le C g(x)\) for all \(x \in \mathbb R^n\).
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Picon, T., Vasconcelos, C. On the Continuity of Strongly Singular Calderón–Zygmund-Type Operators on Hardy Spaces. Integr. Equ. Oper. Theory 95, 9 (2023). https://doi.org/10.1007/s00020-023-02729-4
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DOI: https://doi.org/10.1007/s00020-023-02729-4