A conjecture posed by Chalmoukis in 2020 states that if Tg,a:Hᵖ→ Hq(0<q<p<∞) is bounded, then g must be in Hpq/p-q. In this article, we provide a positive answer to the aforementioned conjecture. We also consider the compactness of Tg,a:Hᵖ→ Hq(0<q<p<∞).
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Yang et al. (2024) studied this question.
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