Small Hankel operators on weighted Besov spaces

Chen Li; Kai Wang

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arXiv · 2611.03901

Small Hankel operators on weighted Besov spaces

Chen Li·Kai Wang

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Abstract

We characterize bounded small Hankel operators from $B_p(\om)$ to $\overline{B_q(\om)}$ on the polydisc for $0<p,q<\infty$, under explicit conditions relating the kernel parameter to the weight. When $q<p$, boundedness is equivalent to a weighted Besov condition on the symbol; when $p\le q$, it is equivalent to a weighted supremum condition on a shifted radial derivative. In particular, the diagonal case is characterized by the product Bloch space. The proof combines weighted Bergman duality and atomic factorization with local kernel estimates and randomized atomic tests.

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BibTeX RIS

Chen Li, Kai Wang. 2026-11-02. Small Hankel operators on weighted Besov spaces. https://arxiv.org/abs/2611.03901

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