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arXiv · 1904.00359

Volterra type integration operators from Bergman spaces to Hardy spaces

Santeri Miihkinen·Jordi Pau·Antti Perälä·Maofa Wang
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Abstract

We completely characterize the boundedness of the Volterra type integration operators $J_b$ acting from the weighted Bergman spaces $A^p_\alpha$ to the Hardy spaces $H^q$ of the unit ball of $\mathbb{C}^n$ for all $0<p,q<\infty$. A partial solution to the case $n=1$ was previously obtained by Z. Wu in \cite{Wu}. We solve the cases left open there and extend all the results to the setting of arbitrary complex dimension $n$. Our tools involve area methods from harmonic analysis, Carleson measures and Kahane-Khinchine type inequalities, factorization tricks for tent spaces of sequences, as well as techniques and integral estimates related to Hardy and Bergman spaces.

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Santeri Miihkinen, Jordi Pau, Antti Perälä, Maofa Wang. 2019-03-31. Volterra type integration operators from Bergman spaces to Hardy spaces. https://arxiv.org/abs/1904.00359

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