Weighted norm inequalities of area operators
Studia Mathematica
MSC: Primary 47B38; Secondary 42B25, 42B35
DOI: 10.4064/sm240720-14-1
Published online: 21 March 2025
Abstract
This paper is devoted to the study of area operators, which originated from research in complex analysis. Using the geometric property of the Carleson measures, we show that the area operators induced by Carleson measures are of weak type $(1,1)$ and of strong type $(p,p)$ for harmonic functions in terms of the Muckenhoupt conditions. Our results also include the case of real variable. The main difficulty lies in the fact that the ideas in complex analysis are not applicable to our setting. The main tool is the generalized Littlewood–Paley functions.
