- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 09:33:52
12
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RMI&vol=22&iss=2&update_since=2024-03-29
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
22
2006
2
Arithmetic properties of positive integers with fixed digit sum
Florian
Luca
UNAM, Campus Morelia, MORELIA, MICHOACÁN, MEXICO
Sum of digits, smooth numbers, subspace theorem, linear forms in logarithms
In this paper, we look at various arithmetic properties of the set of those positive integers $n$ whose sum of digits in a fixed base $b>1$ is a fixed positive integers $s$. For example, we prove that such integers can have many prime factors, that they are not very smooth, and that most such integers have a large prime factor dividing the value of their Euler $\phi$ function.
Number theory
General
369
412
10.4171/RMI/461
http://www.ems-ph.org/doi/10.4171/RMI/461
Genus 3 normal coverings of the Riemann sphere branched over 4 points
Yolanda
Fuertes
Universidad Autónoma de Madrid, MADRID, SPAIN
Manfred
Streit
, OBERURSEL, GERMANY
Moduli of algebraic curves with automorphisms, Weierstrass points, uniform Belyi functions
In this paper we study the 5 families of genus 3 compact Riemann surfaces which are normal coverings of the Riemann sphere branched over 4 points from very different aspects: their moduli spaces, the uniform Belyi functions that factorize through the quotient by the automorphism groups and the Weierstrass points of the non hyperelliptic families.
Algebraic geometry
General
413
454
10.4171/RMI/462
http://www.ems-ph.org/doi/10.4171/RMI/462
Superposition operators and functions of bounded p-variation
Gérard
Bourdaud
Université Pierre et Marie Curie, PARIS CEDEX 05, FRANCE
Massimo
Lanza de Cristoforis
Università di Padova, PADOVA, ITALY
Björn
Schmalfuss
Friedrich-Schiller-Universität Jena, JENA, GERMANY
Functions of bounded p-variation, homogeneous and inhomogeneous Besov spaces, Peetre’s embedding theorem, boundedness of superposition operators
We characterize the set of all functions $f$ of $\mathbb R$ to itself such that the associated superposition operator $T_f: g \to f \circ g$ maps the class $BV^1_p (\mathbb R)$ into itself. Here $BV^1_p (\mathbb R)$, $1 \le p < \infty$, denotes the set of primitives of functions of bounded $p$-variation, endowed with a suitable norm. It turns out that such an operator is always bounded and sublinear. Also, consequences for the boundedness of superposition operators defined on Besov spaces $B^s_{p,q}({\mathbb R}^n)$ are discussed.
Functional analysis
Operator theory
General
455
487
10.4171/RMI/463
http://www.ems-ph.org/doi/10.4171/RMI/463
Poches de tourbillon singulières dans un fluide faiblement visqueux
Taoufik
Hmidi
Université de Rennes 1, RENNES CEDEX, FRANCE
Navier-Stokes and Euler equations, singular vortex patches, inviscid limit, Littlewood-Paley theory
In this paper, we study the singular vortex patches in the two-dimensional incompressible Navier-Stokes equations. We show, in particular, that if the initial vortex patch is $C^{1+s}$ outside a singular set $\Sigma$, so the velocity is, for all time, lipschitzian outside the image of $\Sigma$ through the viscous flow. In addition, the correponding lipschitzian norm is independant of the viscosity. This allows us to prove some results related to the inviscid limit for the geometric structures of the vortex patch.
Partial differential equations
Fluid mechanics
General
489
543
10.4171/RMI/464
http://www.ems-ph.org/doi/10.4171/RMI/464
A geometry on the space of probabilities I. The finite dimensional case
Henryk
Gzyl
Universidad Carlos III, MADRID-GETAFE, SPAIN
Lázaro
Recht
Universidad Simón Bolívar, CARACAS, VENEZUELA
C*-algebra, reductive homogeneous space, lifting of geodesics, exponential families, maximum entropy method
In this note we provide a natural way of defining exponential coordinates on the class of probabilities on the set $\Omega = [1,n]$ or on $\mathbb{P} = \{p=(p_1,\dots,p_n)\in \mathbb{R}^n | p_i > 0; \Sigma_{i=1}^n p_i =1\}$. For that we have to regard $\mathbb{P}$ as a projective space and the exponential coordinates will be related to geodesic flows in $\mathbb{C}^n$.
Functional analysis
Differential geometry
Probability theory and stochastic processes
General
545
558
10.4171/RMI/465
http://www.ems-ph.org/doi/10.4171/RMI/465
The existence of positive solution to some asymptotically linear elliptic equations in exterior domains
Gongbao
Li
Huazhong Normal University, WUHAN, CHINA
Gao-Feng
Zheng
Huazhong Normal University, WUHAN, CHINA
Asymptotically linear elliptic, exterior domain, algebraic topology argument, positive solution
In this paper, we are concerned with the asymptotically linear elliptic problem $-\Delta u+ \lambda_{0}u=f(u), u\in H_{0}^{1}(\Omega ) $ in an exterior domain $\Omega= \mathbb{R}^{N}\setminus\overline{\mathcal{O}} \left( N\geqslant 3\right) $ with $\mathcal{O}$ a smooth bounded and star-shaped open set, and $\lim_{t\rightarrow +\infty }\frac{ f(t)}{t}=l$, $0
Partial differential equations
General
559
590
10.4171/RMI/466
http://www.ems-ph.org/doi/10.4171/RMI/466
Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds
Xiang-Dong
Li
Chinese Academy of Sciences, BEIJING, CHINA
Bakry-Emery Ricci curvature, diffusion operator, Riesz transform, ultracontractivity
Let $(M, g)$ be a complete Riemannian manifold, $L=\Delta -\nabla \phi \cdot \nabla$ be a Markovian symmetric diffusion operator with an invariant measure $d\mu(x)=e^{-\phi(x)}d\nu(x)$, where $\phi\in C^2(M)$, $\nu$ is the Riemannian volume measure on $(M, g)$. A fundamental question in harmonic analysis and potential theory asks whether or not the Riesz transform $R_a(L)=\nabla(a-L)^{-1/2}$ is bounded in $L^p(\mu)$ for all $10$ and $n > 1$, and satisfies $$ (K+c)^{-}\in L^{{n\over 2}+\epsilon}(M, \mu) $$ for some constants $c\geq 0$ and $\epsilon>0$, where $K(x)$ denotes the lowest eigenvalue of the Bakry-Emery Ricci curvature $Ric(L)=Ric+\nabla^2\phi$ on $T_x M$, i.e., $$ K(x)=\inf\limits\{Ric(L)(v, v): v\in T_x M, \|v\|=1\}, \quad\forall\ x\in M. $$ Examples of diffusion operators on complete non-compact Riemannian manifolds with unbounded negative Ricci curvature or Bakry-Emery Ricci curvature are given for which the Riesz transform $R_a(L)$ is bounded in $L^p(\mu)$ for all $p\geq 2$ and for all $a>0$ (or even for all $a\geq 0$).
Potential theory
Differential geometry
Global analysis, analysis on manifolds
Probability theory and stochastic processes
591
648
10.4171/RMI/467
http://www.ems-ph.org/doi/10.4171/RMI/467
On Falconer’s Distance Set Conjecture
M. Burak
Erdoğan
University of Illinois, URBANA, UNITED STATES
Distance sets, Fourier restriction estimates, Frostman measures
In this paper, using a recent parabolic restriction estimate of Tao, we obtain improved partial results in the direction of Falconer's distance set conjecture in dimensions $d\geq 3$.
Fourier analysis
General
649
662
10.4171/RMI/468
http://www.ems-ph.org/doi/10.4171/RMI/468
How smooth is almost every function in a Sobolev space?
Aurélia
Fraysse
Université Paris Est, CRÉTEIL CEDEX, FRANCE
Stéphane
Jaffard
Université Paris Est, CRÉTEIL CEDEX, FRANCE
Sobolev spaces, Besov spaces, prevalence, Haar-null sets, multifractal functions, Hölder regularity, Hausdorff dimension, wavelet bases
We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.
Measure and integration
Functional analysis
General topology
General
663
682
10.4171/RMI/469
http://www.ems-ph.org/doi/10.4171/RMI/469
A logarithmic Sobolev form of the Li-Yau parabolic inequality
Dominique
Bakry
Université Paul Sabatier, TOULOUSE CEDEX 9, FRANCE
Michel
Ledoux
Université Paul Sabatier, TOULOUSE CEDEX 9, FRANCE
Logarithmic Sobolev inequality, Li-Yau parabolic inequality, heat semigroup, gradient estimate, non-negative curvature, diameter bound
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau parabolic inequality. This new inequality is of interest already in Euclidean space for the standard Gaussian measure. The result may also be seen as an extended version of the semigroup commutation properties under curvature conditions. It may be applied to reach optimal Euclidean logarithmic Sobolev inequalities in this setting. Exponential Laplace differential inequalities through the Herbst argument furthermore yield diameter bounds and dimensional estimates on the heat kernel volume of balls.
Global analysis, analysis on manifolds
Probability theory and stochastic processes
General
683
702
10.4171/RMI/470
http://www.ems-ph.org/doi/10.4171/RMI/470
Time-Frequency Analysis of Sjöstrand’s Class
Karlheinz
Gröchenig
Universität Wien, WIEN, AUSTRIA
Pseudodifferential operators, exotic symbols, Wigner distribution, Gabor frame, short-time Fourier transform, spectral invariance, almost diagonalization, modulation space, Wiener’s Lemma
We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.
Partial differential equations
Operator theory
General
703
724
10.4171/RMI/471
http://www.ems-ph.org/doi/10.4171/RMI/471
Le calcul fonctionnel sous-linéaire dans les espaces de Besov homogènes
Gérard
Bourdaud
Université Pierre et Marie Curie, PARIS CEDEX 05, FRANCE
Yves
Meyer
ENS-Cachan, CACHAN CEDEX, FRANCE
Homogeneous Besov spaces, Composition operators, Bounded variation
On établit l'estimation sous-linéaire $\|f \circ g\| \leq c(f) \|g\|$, la norme étant celle de l'espace de Besov homogène $\dot B^{s,q}_{p}(\mathbb{R}^n)$, où $1\leq p
Functional analysis
Operator theory
General
725
746
10.4171/RMI/472
http://www.ems-ph.org/doi/10.4171/RMI/472