On an extension of the notion of Reedy category

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Sharp A₂ inequality for haar shift operators

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Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Singular integrals on Ahlfors-David regular subsets of the Heisenberg group

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Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

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Weak-type estimates for Haar shift operators: Sharp power on the A(p) characteristic

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Maximal operators and differentiation theorems for sparse sets

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Two weight inequalities for discrete positive operators

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Two weight inequalities for maximal truncations of dyadic Calderón-Zygmund operators

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A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

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Level-wise node size distribution of randomly generated regular trees

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Coefficients of Drinfeld modular forms and Hecke operators

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The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.