Lattice Points.
On the Vitali covering properties of a differentiation basis
La razón geométrica del Teorema Fundamental del Cálculo.
Bounded variation and differentiability of functions.
Disquisitio Numerorum.
Por el giro de una aguja.
A counterexample in operator theory
The purpose of this note is to give an explicit construction of a bounded operator T acting on the space L[0,1] such that |Tf(x)| ≤ ∫ |f(y)| dy for a.e. x ∈ [0.1], and, nevertheless, ||T|| = ∞ for every p < 2. Here || || denotes the norm associated to the Schatten-Von Neumann classes.
Geometric Fourier analysis
In this paper we continue the study of the Fourier transform on , , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of , where is the number of equal angles considered in . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of , , of fixed eccentricity...
B₂[∞]-sequences of square numbers
Fractales de Riemann: números y figuras.
Spherical summation : a problem of E.M. Stein
Writing . E. Stein conjectured for , and . We prove this conjecture. We prove also a.e. We only assume .
Estimates for Wainger's singular integrals along curves.
Weyl sums and atomic energy oscillations.
We extend Van der Corput's method for exponential sums to study an oscillating term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.
Finite time singularities in transport equations with nonlocal velocities and fluxes
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