Eine axiomatische Charakterisierung der Hilbert-Transformation
Endpoint boundedness for multilinear integral operators of some sublinear operators on Herz and Herz type Hardy spaces.
Endpoint bounds for convolution operators with singular measures
Let be the graph of the function defined by with 1< and let the measure on induced by the Euclidean area measure on S. In this paper we characterize the set of pairs (p,q) such that the convolution operator with is - bounded.
Endpoint estimates and weighted norm inequalities for commutators of fractional integrals.
Endpoint estimates for multilinear commutator of Marcinkiewicz operator.
Entropy bump conditions for fractional maximal and integral operators
We investigate weighted inequalities for fractional maximal operators and fractional integral operators.We work within the innovative framework of “entropy bounds” introduced by Treil–Volberg. Using techniques developed by Lacey and the second author, we are able to efficiently prove the weighted inequalities.
Ergodic theory and connections with analysis and probability.
Errata of the paper “On the - boundedness of some fractional integral operators”
Estimates for differential operators of vector analysis involving -norm
Estimates for maximal singular integrals
It is shown that maximal truncations of nonconvolution L²-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1,1) and -bounded for 1 < p< ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the boundedness of such maximal singular integral operators in an alternative way.
Estimates for oscillatory singular integrals on Hardy spaces
For any n ∈ ℕ, we obtain a bound for oscillatory singular integral operators with polynomial phases on the Hardy space H¹(ℝⁿ). Our estimate, expressed in terms of the coefficients of the phase polynomial, establishes the H¹ boundedness of such operators in all dimensions when the degree of the phase polynomial is greater than one. It also subsumes a uniform boundedness result of Hu and Pan (1992) for phase polynomials which do not contain any linear terms. Furthermore, the bound is shown to be valid...
Estimates for Singular Convolution Operators on the Heisenberg Group.
Estimates for singular integral operators in terms of maximal functions
Estimates for singular integral operators with mixed type homogeneities in Hardy classes.
Estimates for singular integrals and extrapolation
We study singular integrals with rough kernels, which belong to a class of singular Radon transforms. We prove certain estimates for the singular integrals that are useful in an extrapolation argument. As an application, we prove boundedness of the singular integrals under a certain sharp size condition on their kernels.
Estimates for Wainger's singular integrals along curves.
Estimates of BMO type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDEs.
Estimates of one-dimensional oscillatory integrals
We study one-dimensional oscillator integrals which arise as Fourier-Stieltjes transforms of smooth, compactly supported measures on smooth curves in Euclidean spaces and determine their decay at infinity, provided the curves satisfy certain geometric conditions.
Estimations pour les noyaux singuliers
Estimations d’intégrales oscillantes