Matrix weights and a maximal function with exponent 3/2

Abstract

We build an example of a simple sparse operator for which its norm with scalar A 2 weight has linear estimate in [w]A2 ${\left[w\right]}_{{A}_{2}}$ , but whose norm in matrix setting grows at least as [W]A23/2 ${\left[W\right]}_{{\mathbf{A}}_{2}}^{3/2}$ for specially constructed weights from A 2. We also demonstrate a matrix weighted maximal function with the same estimate from below.

Keywords

• matrix weights
• convex body maximal functions
• sparse family
• matrix weighted maximal function
• 42b20
• 42b35
• 47a30