arxiv:2402.06961v1 [math.CA] 10 Feb 2024 Page 1 THE MATRIX A2 CONJECTURE FAILS, IE
3/2 > 1. KOMLA DOMELEVO, STEFANIE PETERMICHL, SERGEI TREIL, AND ALEXANDER …

We prove a quantified sparse bound for the maximal truncations of convolution-type singular
integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination …

We will introduce the basics of dyadic harmonic analysis and how it can be used to obtain
weighted estimates for classical Calderón–Zygmund singular integral operators and their …

In this paper we extend the theory of two weight, A_p A p bump conditions to the setting of
matrix weights. We prove two matrix weight inequalities for fractional maximal operators …

Let p∈(1,∞), ρ∈(2,∞) and W be a matrix A p weight. In this paper, we introduce a version of
variation 𝒱 ρ (𝒯 n,∗) for matrix Calderón–Zygmund operators with modulus of continuity …

We prove Poincaré and Sobolev inequalities inmatrix A p weighted spaces. We then use
these Poincaré inequalities to prove existence and regularity results for degenerate systems …

We develop a biparameter theory for matrix weights and provide various biparameter matrix-
weighted bounds for Journé operators as well as other central operators under the …

In this paper, we approach the two weighted boundedness of commutators via matrix
weights. This approach provides both a sufficient and a necessary condition for the two …

We prove the matrix $ A_2 $ conjecture for the dyadic square function, that is, a norm
estimate of the matrix weighted square function, where the focus is on the sharp linear …

Let W denote a matrix A 2 weight. In this paper, we implement a scalar argument using the
square function to deduce related bounds for vector-valued functions in L 2 (W). These …