On a generalization of Fueter's theorem.
On a singular integral
On a singular integral
On an extension of singular integrals along manifolds of finite type.
On an inequality of Sagher and Zhou concerning Stein's lemma.
On approach regions for the conjugate Poisson integral and singular integrals
Let ũ denote the conjugate Poisson integral of a function . We give conditions on a region Ω so that , the Hilbert transform of f at x, for a.e. x. We also consider more general Calderón-Zygmund singular integrals and give conditions on a set Ω so that is a bounded operator on , 1 < p < ∞, and is weak (1,1).
On approximate differentiability of functions with bounded deformation.
On Bojarski's index formula for nonsmooth interfaces.
On Calderón's conjecture.
On certain estimates for Marcinkiewicz integrals and extrapolation.
On certain hypersingular integrals
On certain nonstandard Calderón-Zygmund operators
We formulate a version of the T1 theorem which enables us to treat singular integrals whose kernels need not satisfy the usual smoothness conditions. We also prove a weighted version. As an application of the general theory, we consider a class of multilinear singular integrals in related to the first Calderón commutator, but with a kernel which is far less regular.
On certain rough integral operators and extrapolation.
On conjugate Poisson integrals and Riesz transforms for the Hermite expansions
On Entropy Bumps for Calderón-Zygmund Operators
We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ℇ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on Rd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound [...]
On Entropy Bumps for Calderón-Zygmund Operators
We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).
On ergodic singular integral operators
On extrapolation blowups in the scale.
On Hardy spaces in complex ellipsoids
This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define with respect to a certain measure that degenerates near Levi-flat points...
On Higher Riesz Transforms for Gaussian Measures.