${\hat{I}}^2$-dimensional sharp maximal function and applications

You-Wei Benson Chen, Alejandro Claros

In this paper, we study ${\hat{I}}^2$-dimensional sharp maximal operator defined as \begin{align*} \mathcal{M}^{\#} _βf(x) := \sup_{Q} \inf_{c \in \mathbb{R}} χ_{Q}(x) \frac{1}{\ell(Q)^β…