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arXiv · 2509.03158

Fractional integral on Hardy spaces on product domains

Yiyu Tang
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Abstract

By using the vector-valued theory of singular integrals, we prove a Hardy--Littlewood--Sobolev inequality on product Hardy spaces $H^p_{\rm{prod}}$, which is a parallel result of the classical Hardy--Littlewood--Sobolev inequality. The same technique shows the $H^p_{\rm{prod}}$-boundedness of the iterated Hilbert transform. As a byproduct, new proofs of several recently discovered Hardy type inequalities on product Hardy spaces are obtained, which avoid complicated Calder\'on--Zygmund theory on product domain, rendering them considerably simpler than the original proofs.

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Yiyu Tang. 2025-09-03. Fractional integral on Hardy spaces on product domains. https://arxiv.org/abs/2509.03158

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