Singular integrals with highly oscillating kernels on the product domains
Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves
The paper presents a theory of Fourier transforms of bounded holomorphic functions defined in sectors. The theory is then used to study singular integral operators on star-shaped Lipschitz curves, which extends the result of Coifman-McIntosh-Meyer on the -boundedness of the Cauchy integral operator on Lipschitz curves. The operator theory has a counterpart in Fourier multiplier theory, as well as a counterpart in functional calculus of the differential operator 1/i d/dz on the curves.
Singular kernels supported by homogeneous submanifolds.
Singular Radon transforms and maximal functions under convexity assumptions.
We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal functions along convex curves in the plane.
Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator
2000 Mathematics Subject Classification: 42B20, 42B25, 42B35We consider the generalized shift operator, generated by the Laplace- Bessel differential operator [...] The Bn -maximal functions and the Bn - Riesz potentials, generated by the Laplace-Bessel differential operator ∆Bn are investigated. We study the Bn - Riesz potentials in the Bn - Morrey spaces and Bn - BMO spaces. An inequality of Sobolev - Morrey type is established for the Bn - Riesz potentials.* This paper has been partially supported...
Solution of some weight problems for the Riemann-Liouville and Weyl operators.
Solution of two-weight problems for integral transforms with positive kernels.
Some estimates for commutators of Riesz transform associated with Schrödinger type operators
Let be a Schrödinger operator and let be a Schrödinger type operator on , where is a nonnegative potential belonging to certain reverse Hölder class...
Some Hardy spaces estimates for multilinear Littlewood-Paley -operators.
Some integral and maximal operators related to starlike sets
We prove two-weight norm estimates for fractional integrals and fractional maximal functions associated with starlike sets in Euclidean space. This is seen to include general positive homogeneous fractional integrals and fractional integrals on product spaces. We consider both weak type and strong type results, and we show that the conditions imposed on the weight functions are fairly sharp.
Some new light on a few classical results
The purpose of this paper is to describe a unified approach to proving vector-valued inequalities without relying on the full strength of weighted theory. Our applications include the Fefferman-Stein and Córdoba-Fefferman inequalities, as well as the vector-valued Carleson operator. Using this approach we also produce a proof of the boundedness of the classical bi-parameter multiplier operators, which does not rely on product theory. Our arguments are inspired by the vector-valued restricted type...
Some remarks on Bochner-Riesz means
We study norm convergence of Bochner-Riesz means associated with certain non-negative differential operators. When the kernel satisfies a weak estimate for large values of m we prove norm convergence of for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.
Some sharp weighted estimates for multilinear operators.
Spaces and on - groups.
Spaces of bounded λ-central mean oscillation, Morrey spaces, and λ-central Carleson measures.
Spherical means and measures with finite energy
We prove a restricted weak type inequality for the spherical means operator with respect to measures with finite α-energy, α ≤ 1. This complements recent results due to D. Oberlin.
Square functions of Calderón type and applications.
We establish L2 and Lp bounds for a class of square functions which arises in the study of singular integrals and boundary value problems in non-smooth domains. As an application, we present a simplified treatment of a class of parabolic smoothing operators which includes the caloric single layer potential on the boundary of certain minimally smooth, non-cylindrical domains.
Sufficient Conditions for One-Sided Operators.
Symbol calculus on the affine group "ax + b"
The symbol calculus on the upper half plane is studied from the viewpoint of the Kirillov theory of orbits. The main result is the -estimates for Fuchs type pseudodifferential operators.
Tb theorems for Triebel-Lizorkin spaces over special spaces of homogeneous type and their applications