paper

Embedding theorems and integration operators on Hardy--Carleson type tent spaces induced by doubling weights

arXiv:2602.02049

Abstract

This paper develops the function and operator theory of Hardy--Carleson--type analytic tent spaces $A T_{q}^{\infty} (I ¨ )$ induced by radial weights $I ¨ $ satisfying a two-sided doubling condition. We first characterize the positive Borel measures $I^¼$ for which the embedding from $A T_{p}^{\infty} (I ¨ )$ into the tent space $T_{q}^{\infty} (I^¼)$ is bounded for all $0 < p, q < \infty$ . A Littlewood--Paley formula for $A T_{q}^{\infty} (I ¨ )$ is then established. Using these results, we give a complete characterization of the boundedness (compactness) of Volterra-type integration operators between $A T_{p}^{\infty} (I ¨ )$ and $A T_{q}^{\infty} (I ¨ )$ .