1130 NOTICES OF THE AMS VOLUME 45, NUMBER 9 T he subject matter of this essay is Alberto Calderón’s pivotal role in the creation of the modern theory of singular integrals. In that great enterprise Calderón had the good fortune of working with Antoni Zygmund, who was at first his teacher and mentor and later his collaborator. For that reason any account of that theory has to be in part the stor...

Two versions of Rubio de Francia’s extrapolation theorem for multivariable operators of functions are obtained. One version assumes an initial estimate with different weights in each space and implies boundedness on all products of Lebesgue spaces. Another version assumes an initial estimate with the same weight but yields boundedness on a product of Lebesgue spaces whose indices lie on a line....

Abstract. Given a doubling measure μ on R, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L(μ) are also of weak type (1, 1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit...

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...

We prove a Calderón-Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators and generalized Radon transforms.

In this paper, we establish the boundedness of commutators generated by weighted Lipschitz functions and Calderón-Zygmund singular integral operators on weighted Herz spaces.

In this paper, the authors study the boundedness of multilinear Calderón-Zygmund singular integral operators and their commutators in generalized Morrey spaces.

Calderón-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general which admit Markov semigroup purely algebraic assumptions. We shall construct an abstract form ‘Markov metric’ governing process and naturally associated BMO spaces, interpolate with Lp-scale endpoint ...