THE SHARP SQUARE FUNCTION ESTIMATE WITH MATRIX WEIGHT

Tuomas Hytönen (1) , Stefanie Petermichl (2) , Alexander Volberg (3)

1 Helsingin yliopisto = Helsingfors universitet = University of Helsinki
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 Michigan State University [East Lansing]

We prove the matrix A 2 conjecture for the dyadic square function, that is, an estimate of the form S W L 2 C d (W)→L 2 R [W ] A 2 , where the focus is on the sharp linear dependence on the matrix A 2 constant. Moreover, we give a mixed estimate in terms of A 2 and A∞ constants. Key is a sparse domination of a process inspired by the integrated form of the matrix-weighted square function.

Domaines: Mathématiques [math]; Analyse classique [math.CA]

Tuomas Hytönen, Stefanie Petermichl, Alexander Volberg. THE SHARP SQUARE FUNCTION ESTIMATE WITH MATRIX WEIGHT. Discrete Analysis, 2019. ⟨hal-01977600⟩