Let R be the vector of Riesz transforms on\mathbb R^ n R n, and let μ, λ ∈ A_p μ, λ∈ A p be
two weights on\mathbb R^ n R n, 1< p< ∞ 1< p<∞. The two-weight norm inequality for the …

Let σ and ω be locally finite positive Borel measures on R n with no common point masses,
and let Tα be a standard α-fractional Calderón–Zygmund operator on R n with 0≤ α< n …

Let μ be a positive locally finite Borel measure on R n that is doubling, and define the
homogeneous W s μ-Sobolev norm squared f W s μ 2 of a function f∈ L loc 2 μ by∫ R n∫ R …

This paper is a sequel to our paper Sawyer et al.(Revista Mat Iberoam 32 (1): 79–174,
2016). Let σ and ω be locally finite positive Borel measures on ℝ n R^ n (possibly having …

In this paper we construct a wavelet basis in L^ 2 (R^ n; μ) L 2 (R n; μ) possessing vanishing
moments of a fixed order for a general locally finite positive Borel measure μ μ. The …

Let σ and ω be locally finite positive Borel measures on R^ n, let T α be a standard α-
fractional Calderón-Zygmund operator on R^ n with 0≤ α< n, and assume as side …

arXiv:2111.06277v4 [math.CA] 26 Sep 2022 Page 1 arXiv:2111.06277v4 [math.CA] 26 Sep
2022 A T1 THEOREM FOR GENERAL SMOOTH CALDERON-ZYGMUND OPERATORS WITH …

If T is a smooth Stein elliptic fractional singular integral, 1< p< infinity, and sigma and omega
are doubling measures, then the two weight L^{p} norm inequality holds if and only if the …

We show that the energy conditions are not necessary for boundedness of fractional Riesz
transforms in dimension at least 2. We also give a weak converse, namely that the energy …

We begin an investigation into extending the T 1 theorem of David and Journé, and the
corresponding optimal cancellation conditions of Stein, to more general pairs of distinct …