English

Sharp matrix weighted strong type inequalities for the dyadic square function

Classical Analysis and ODEs 2019-05-09 v2

Abstract

In this paper we refine the recent sparse domination of the integrated p=2p = 2 matrix weighted dyadic square function by T. Hytonen, S. Petermichl, and A. Volberg to prove a pointwise sparse domination of general matrix weighted dyadic square functions. We then use this to prove sharp two matrix weighted strong type inequalities for matrix weighted dyadic square functions when 1<p21 < p \leq 2.

Cite

@article{arxiv.1901.10150,
  title  = {Sharp matrix weighted strong type inequalities for the dyadic square function},
  author = {Joshua Isralowitz},
  journal= {arXiv preprint arXiv:1901.10150},
  year   = {2019}
}

Comments

11 pages, no figures, submitted, the proofs of the sharp weak type estimates in Theorems 1.2 and 1.3 in the first version had an error that we could not fix, and therefore are omitted in this version (and remain open). The title and abstract has been changed to reflect this

R2 v1 2026-06-23T07:25:11.871Z