An atomic theory of ergodic spaces
An endpoint estimate for some maximal operators.
An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices
We show that for every there exists a weight such that the Lorentz Gamma space is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space and on its associate space .
An example on the maximal function associated to a nondoubling measure.
We show that there is a measure y defined on the hyperbolic plane and with polynomial growth, such that the centered maximal operator associated to y does not satisfy weak type (1, 1) bounds.
An exponential estimate for convolution powers
We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.
An improved bound for Kakeya type maximal functions.
The purpose of this paper is to improve the known results (specifically [1]) concerning Lp boundedness of maximal functions formed using 1 x δ x ... x δ tubes.
An improved bound on the Minkowski dimension of Besicovitch sets in .
An improved maximal inequality for 2D fractional order Schrödinger operators
The local maximal operator for the Schrödinger operators of order α > 1 is shown to be bounded from to L² for any s > 3/8. This improves the previous result of Sjölin on the regularity of solutions to fractional order Schrödinger equations. Our method is inspired by Bourgain’s argument in the case of α = 2. The extension from α = 2 to general α > 1 faces three essential obstacles: the lack of Lee’s reduction lemma, the absence of the algebraic structure of the symbol and the inapplicable...
An inequality for measures on a half-space.
An inequality for the Hardy-Littlewood maximal operator with respect to a product of differentiation bases
An interpolation theorem with -weighted spaces
An X-ray transform estimate in Rn.
We prove an x-ray estimate in general dimension which is a stronger version of Wolff's Kakeya estimate [12]. This generalizes the estimate in [13], which dealt with the n = 3 case.
Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms
We study spectral properties of transfer operators for diffeomorphisms on a Riemannian manifold . Suppose that is an isolated hyperbolic subset for , with a compact isolating neighborhood . We first introduce Banach spaces of distributions supported on , which are anisotropic versions of the usual space of functions and of the generalized Sobolev spaces , respectively. We then show that the transfer operators associated to and a smooth weight extend boundedly to these spaces, and...
Anisotropic symmetrization
Applicationsof Generalized Perron Trees to Maximal Functions and Density Bases.
Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces
If the Poisson integral of the unit disc is replaced by its square root, it is known that normalized Poisson integrals of and weak boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning and the author, respectively. In this paper we characterize the approach regions for boundary functions in two general classes of Orlicz spaces. The first of these classes contains spaces having the property , . The second contains spaces that...
Approximation of commutators of singular integrals
Approximation of Distribution Spaces by Means of Kernel Operators.
Area integral estimates for higher order elliptic equations and systems
Let be an elliptic system of higher order homogeneous partial differential operators. We establish in this article the equivalence in norm between the maximal function and the square function of solutions to in Lipschitz domains. Several applications of this result are discussed.
Averages of functions over hypersurfaces in Rn.