Maximal functions and singular integrals associated to polynomial mapping of Rn.
Maximal functions related to subelliptic operators with polynomially growing coefficients.
Maximal inequalities and Riesz transform estimates on spaces for Schrödinger operators with nonnegative potentials
We show various estimates for Schrödinger operators on and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of and their gradients.
Maximal operators defined by Fourier multipliers
Maximal operators, Lebesgue points and quasicontinuity in strongly nonlinear potential theory.
Maximal regularity and Hardy spaces
Maximal singular integrals on product homogeneous groups
We prove boundedness for p ∈ (1,∞) of maximal singular integral operators with rough kernels on product homogeneous groups under a sharp integrability condition of the kernels.
Mean Oscillation and Boundedness of Multilinear Integral Operators with General Kernels
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are proved. The integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.
Mean Oscillation of Functions and the Paley-Wiener Space.
Mean Quadratic Variations and Fourier Asymptotics of Self-similar Measures.
Measure-geometric Laplacians for partially atomic measures
Motivated by the fundamental theorem of calculus, and based on the works of W. Feller as well as M. Kac and M. G. Kreĭn, given an atomless Borel probability measure supported on a compact subset of U. Freiberg and M. Zähle introduced a measure-geometric approach to define a first order differential operator and a second order differential operator , with respect to . We generalize this approach to measures of the form , where is non-atomic and is finitely supported. We determine analytic...
Measure-preserving quality within mappings.
In [6], Guy David introduced some methods for finding controlled behavior in Lipschitz mappings with substantial images (in terms of measure). Under suitable conditions, David produces subsets on which the given mapping is bilipschitz, with uniform bounds for the bilipschitz constant and the size of the subset. This has applications for boundedness of singular integral operators and uniform rectifiability of sets, as in [6], [7], [11], [13]. Some special cases of David's results, concerning projections...
Meda inequality for rearrangements of the convolution on the Heisenberg group and some applications.
Medians, continuity, and vanishing oscillation
We consider properties of medians as they pertain to the continuity and vanishing oscillation of a function. Our approach is based on the observation that medians are related to local sharp maximal functions restricted to a cube of ℝⁿ.
Micro-Local Analysis in Some Spaces of Ultradistributions
Mikhlin's problem on Carnot groups.
Minimal rearrangements of Sobolev functions
Mixed estimates with one supremum
We establish several mixed bounds for Calderón-Zygmund operators that only involve one supremum. We address both cases when the part of the constant is measured using the exponential-logarithmic definition and using the Fujii-Wilson definition. In particular, we answer a question of the first author and provide an answer, up to a logarithmic factor, to a conjecture of Hytönen and Lacey. Moreover, we give an example to show that our bounds with the logarithmic factors can be arbitrarily smaller...
Mixed K-Functionals: A Measure of Smoothness for Blending-type Approximation.
Möbius invariance of analytic Besov spaces in tube domains over symmetric cones
Besov spaces of holomorphic functions in tubes over cones have been recently defined by Békollé et al. In this paper we show that Besov p-seminorms are invariant under conformal transformations of the domain when n/r is an integer, at least in the range 2-r/n < p ≤ ∞.