Sharp Lorentz-norm estimates for dyadic-like maximal operators
Volume 257 / 2021
Studia Mathematica 257 (2021), 87-110
MSC: Primary 42B25; Secondary 60G42.
DOI: 10.4064/sm191111-24-5
Published online: 6 August 2020
Abstract
For any $1 \lt p \le q_1 \lt q_2 \lt \infty $, we identify the norm of the dyadic maximal operator on $\mathbb R ^n$ as an operator from $L^{p,q_1}$ to $L^{p,q_2}$. A related statement for general measure spaces equipped with tree-like structure is also established. The proof rests on the identification of an explicit formula for the associated Bellman function, which requires novel ideas due to the nonintegral form of Lorentz norms.
