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arXiv · 2405.19372

On a conjecture about generalized integration operators on Hardy spaces

Rong Yang·Songxiao Li
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Abstract

A conjecture posed by Chalmoukis in 2020 states that if $T_{g,a}:H^p\to H^q(0<q<p<\infty)$ is bounded, then $g$ must be in $H^{\frac{pq}{p-q}}$. In this article, we provide a positive answer to the aforementioned conjecture. We also consider the compactness of $T_{g,a}:H^p\to H^q(0<q<p<\infty)$.

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Rong Yang, Songxiao Li. 2024-05-28. On a conjecture about generalized integration operators on Hardy spaces. https://arxiv.org/abs/2405.19372

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