Sharp Lp estimates for the segment multiplier.
Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications
In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates which do...
Sharp spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates
We consider an abstract non-negative self-adjoint operator L acting on L²(X) which satisfies Davies-Gaffney estimates. Let (p > 0) be the Hardy spaces associated to the operator L. We assume that the doubling condition holds for the metric measure space X. We show that a sharp Hörmander-type spectral multiplier theorem on follows from restriction-type estimates and Davies-Gaffney estimates. We also establish a sharp result for the boundedness of Bochner-Riesz means on .
Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms
We study sharp weak-type inequalities for a wide class of Fourier multipliers resulting from modulation of the jumps of Lévy processes. In particular, we obtain optimal estimates for second-order Riesz transforms, which lead to interesting a priori bounds for smooth functions on ℝd. The proofs rest on probabilistic methods: we deduce the above inequalities from the corresponding estimates for martingales. To obtain the lower bounds, we exploit the properties of laminates, important probability measures...
Sharp weighted inequalities for vector-valued multilinear commutators of Marcinkiewicz operator.
Singular Cauchy integrals and conformal welding on Jordan curves.
Singular integral operators on manifolds with a boundary.
Singular integral operators on Nakano spaces with weights having finite sets of discontinuities
In 1968, Gohberg and Krupnik found a Fredholm criterion for singular integral operators of the form aP + bQ, where a,b are piecewise continuous functions and P,Q are complementary projections associated to the Cauchy singular integral operator, acting on Lebesgue spaces over Lyapunov curves. We extend this result to the case of Nakano spaces (also known as variable Lebesgue spaces) with certain weights having finite sets of discontinuities on arbitrary Carleson curves.
Singular integral operators with Cauchy kernel in fractional spaces.
Singular integral operators with non-smooth kernels on irregular domains.
Let χ be a space of homogeneous type. The aims of this paper are as follows.i) Assuming that T is a bounded linear operator on L2(χ), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(χ) for 1 < p ≤ 2; our condition is weaker then the usual Hörmander integral condition.ii) Assuming that T is a bounded linear operator on L2(Ω) where Ω is a measurable subset of χ, we give a sufficient condition on the kernel of T so that T is of weak type...
Singular Integrals, Analytic Capacity and Rectifiability.
Singular integrals and rectifiability.
We shall discuss singular integrals on lower dimensional subsets of Rn. A survey of this topic was given in [M4]. The first part of this paper gives a quick review of some results discussed in [M4] and a survey of some newer results and open problems. In the second part we prove some results on the Riesz kernels in Rn. As far as I know, they have not been explicitly stated and proved, but they are very closely related to some earlier results and methods.[Proceedings of the 6th International Conference...
Singular integrals and spherical convergence
Singular Integrals in the Cesàro Sense.
Singular integrals in weighted Lebesgue spaces with variable exponent.
Singular integrals on
Singular integrals on generalized Lipschitz and Hardy spaces
Singular integrals on Iwasawa NA groups of rank 1.
Singular integrals on Sierpinski gaskets .
Singular integrals on the complex affine group