Joshua Isralowitz

Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols

Let B be a locally integrable matrix function, W a matrix Ap weight with 1<p<∞, and T be any of the Riesz transforms. We will characterize the boundedness of the commutator [T,B] on Lp(W) in terms of the membership of B in a natural matrix weighted BMO space. To do this, we will characterize the boundedness of dyadic paraproducts on Lp(W) via a new matrix weighted Carleson embedding theorem. Finally, we will use some of the ideas from these proofs to (among other things) obtain quantitative weighted norm inequalities for these operators and also use them to prove sharp L2 bounds for the Christ/Goldberg matrix weighted maximal function associated with matrix A2 weights.

Toeplitz Operators on Fock–Sobolev Type Spaces

In this paper, we characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on weighted Fock–Sobolev spaces of fractional order.

A Matrix Weighted T1 Theorem for Matrix Kernelled CZOs and a Matrix Weighted John–Nirenberg Theorem

In this paper, we will prove a matrix weighted T1 theorem regarding the boundedness of certain matrix kernelled CZOs on matrix weighted

Two Weight Bump Conditions for Matrix Weights

L^p(W)

Schatten class Toeplitz operators on generalized Fock spaces

Lp(W) for matrix A

A matrix weighted

{}_p