Mean-periodic functions.
Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R
2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63Using a convolution structure on the real line associated with the Jacobi-Dunkl differential-difference operator Λα,β given by: Λα,βf(x) = f'(x) + ((2α + 1) coth x + (2β + 1) tanh x) { ( f(x) − f(−x) ) / 2 }, α ≥ β ≥ −1/2 , we define mean-periodic functions associated with Λα,β. We characterize these functions as an expansion series intervening appropriate elementary functions expressed in terms of the derivatives of the...
Mean-periodicity and zeta functions
This paper establishes new bridges between zeta functions in number theory and modern harmonic analysis, namely between the class of complex functions, which contains the zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of an arithmetic scheme with its expected analytic shape is shown...
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...
Measures and lacunary sets
We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.
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.
Meixner-type results for Riordan arrays and associated integer sequences.
Mellin pseudodifferential operators with slowly varying symbols and singular integrals on Carleson curves with Muckenhoupt weights.
Mémoire sur l'approximation des fonctions de très-grands nombres, et sur une classe étendue de développements en série.
Mesures spectrales associées à certaines suites arithmétiques
Mesures spectrales de Walsh associées à certaines suites arithmétiques
On associe à certaines suites de nombres complexes une mesure borélienne positive sur le tore dont la transformée de Fourier-Walsh est une suite de moyennes liées à . La nature de (discrète, continue) est discutée dans quelques cas : suites presque-périodiques et certaines suites arithmétiques.
Metric unconditionality and Fourier analysis
We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces and of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between and . These...
Micro-Local Analysis in Some Spaces of Ultradistributions
Mikhlin's problem on Carnot groups.
Minimal rearrangements of Sobolev functions
Minimal sequences and the Kadison-Singer problem.
Minimale Elemente auf Hyperebenen und konjugierte Funktionen
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...