- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 11:42:10
9
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RMI&vol=18&iss=3&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)
18
2002
3
Outer and inner vanishing measures and division in $H^\infty + C$
Keiji
Izuchi
Niigata University, NIIGATA, JAPAN
Singular inner function, bounded analytic function, $H^\infty + C$
Measures on the unit circle are well studied from the view of Fourier analysis. In this paper, we investigate measures from the view of Poisson integrals and of divisibility of singular inner functions in $H^\infty + C$. Especially, we study singular measures which have outer and inner vanishing measures. It is given two decompositions of a singular positive measure. As applications, it is studied division theorems in $H^\infty + C$.
Functional analysis
General
511
540
10.4171/RMI/327
http://www.ems-ph.org/doi/10.4171/RMI/327
On independent times and positions for Brownian motions
Bernard
de Meyer
Université Henri Poincaré, VANDOEUVRE LES NANCY, FRANCE
Bernard
Roynette
Université Henri Poincaré, VANDOEUVRE LES NANCY, FRANCE
Pierre
Vallois
Université Henri Poincaré, VANDOEUVRE LES NANCY, FRANCE
Marc
Yor
Université Paris VI, PARIS CEDEX 05, FRANCE
Skorokhod embedding, space-time Brownian motion, Ornstein-Uhlenbeck and Bessel processes, Hadamard’s theorem
Let $(B_t ; t \ge 0)$, $\big(\mbox{resp. }((X_t, Y_t) ; t \ge 0)\big)$ be a one (resp. two) dimensional Brownian motion started at 0. Let $T$ be a stopping time such that $(B_{t \wedge T} ; t \ge 0)$ \big(resp. $(X_{t \wedge T} ; t \ge 0) ; (Y_{t \wedge T} ; t \ge 0)\big)$ is uniformly integrable. The main results obtained in the paper are: \begin{itemize} \item[1)] if $T$ and $B_T$ are independent and $T$ has all exponential moments, then $T$ is constant. \item[2)] If $X_T$ and $Y_T$ are independent and have all exponential moments, then $X_T$ and $Y_T$ are Gaussian. \end{itemize} We also give a number of examples of stopping times $T$, with only some exponential moments, such that $T$ and $B_T$ are independent, and similarly for $X_T$ and $Y_T$. We also exhibit bounded non-constant stopping times $T$ such that $X_T$ and $Y_T$ are independent and Gaussian.
Probability theory and stochastic processes
General
541
586
10.4171/RMI/328
http://www.ems-ph.org/doi/10.4171/RMI/328
Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions
Herbert
Koch
Universität Bonn, BONN, GERMANY
Björn
Schmalfuss
Friedrich-Schiller-Universität Jena, JENA, GERMANY
Besov spaces of smoothness zero, pointwise multipliers, paraproducts characteristic, Dini continuous functions, gradient estimates
We characterize the set of pointwise multipliers of the Besov spaces $B^0_{\infty,1}$ and $B^0_{\infty,\infty} $. These characterizations are used to obtain regularity results for elliptic partial differential equations. In addition several counterexamples are provided and the relation of various spaces of continuous functions to these multiplier classes are studied.
Functional analysis
Partial differential equations
General
587
626
10.4171/RMI/329
http://www.ems-ph.org/doi/10.4171/RMI/329
Quasiconformal mappings of $Y$-pieces
Christopher
Bishop
SUNY at Stony Brook, STONY BROOK, UNITED STATES
Hausdorff dimension, quasi-Fuchsian groups, quasiconformal deformation, critical exponent, convex core
In this paper we construct quasiconformal mappings between Y-pieces so that the corresponding Beltrami coefficient has exponential decay away from the boundary. These maps are used in a companion paper to construct quasiFuchsian groups whose limit sets are non-rectifiable curves of dimension 1.
Functions of a complex variable
General
627
652
10.4171/RMI/330
http://www.ems-ph.org/doi/10.4171/RMI/330
Non-rectifiable limit sets of dimension one
Christopher
Bishop
SUNY at Stony Brook, STONY BROOK, UNITED STATES
Hausdorff dimension, quasi-Fuchsian groups, quasiconformal deformation, critical exponent, convex core
We construct quasiconformal deformations of convergence type Fuchsian groups such that the resulting limit set is a Jordan curve of Hausdorff dimension 1, but having tangents almost nowhere. It is known that no divergence type group has such a deformation. The main tools in this construction are (1) a characterization of tangent points in terms of Peter Jones' $\beta$'s, (2) a result of Stephen Semmes that gives a Carleson type condition on a Beltrami coefficient which implies rectifiability and (3) a construction of quasiconformal deformations of a surface which shrink a given geodesic and whose dilatations satisfy an exponential decay estimate away from the geodesic.
Functions of a complex variable
General
653
684
10.4171/RMI/331
http://www.ems-ph.org/doi/10.4171/RMI/331
Lebesgue points for Sobolev functions on metric spaces
Juha
Kinnunen
Aalto University, AALTO UNIVERSITY, FINLAND
Visa
Latvala
University of Joensuu, JOENSUU, FINLAND
Sobolev spaces, spaces of homogeneous type, doubling measures, capacity, regularity, maximal functions
Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the measure is doubling. This result seems to be new even for the weighted Sobolev spaces on Euclidean spaces. The crucial ingredient of our argument is a maximal function related to discrete convolution approximations. In particular, we do not use the Besicovitch covering theorem, extension theorems or representation formulas for Sobolev functions.
Functional analysis
General
685
700
10.4171/RMI/332
http://www.ems-ph.org/doi/10.4171/RMI/332
$L^p$ estimates for singular integrals with kernels belonging to certain block spaces
Hussain
Al-Qassem
Yarmouk University, IRBID, JORDAN
Yibiao
Pan
University of Pittsburgh, PITTSBURGH, UNITED STATES
$L^p$ boundedness, singular integrals, block spaces, maximal operators, Fourier transform, oscillatory integrals
We establish the $L^p$ boundedness of singular integrals with kernels which belong to block spaces and are supported by subvarieties.
Fourier analysis
General
701
730
10.4171/RMI/333
http://www.ems-ph.org/doi/10.4171/RMI/333
Global existence for the discrete diffusive coagulation-fragmentation equations in $L^1$
Philippe
Laurençot
Université de Toulouse, TOULOUSE CEDEX 9, FRANCE
Stéphane
Mischler
Université de Paris-Dauphine, PARIS CEDEX 16, FRANCE
Cluster growth, coalescence, breakage, infinite system of reaction-diffusion equations, existence, weak compactness
Existence of global weak solutions to the discrete coagulation-fragmentation equations with diffusion is proved under general assumptions on the coagulation and fragmentation coefficients. Unlike previous works requiring $L^\infty$-estimates, an $L^1$-approach is developed here which relies on weak and strong compactness methods in $L^1$.
Partial differential equations
Statistical mechanics, structure of matter
General
731
745
10.4171/RMI/334
http://www.ems-ph.org/doi/10.4171/RMI/334
Some questions on quasinilpotent groups and related classes
María Jesús
Iranzo
Universitat de València, BURJASSOT (VALENCIA), SPAIN
Juan
Medina
Universidad Politécnica de Cartagena, CARTAGENA, SPAIN
Francisco
Pérez-Monasor
Universitat de València, BURJASSOT (VALENCIA), SPAIN
Nilpotent group, quasinilpotent group, injector, fusion
In this paper we will prove that if $G$ is a finite group, $X$ a subnormal subgroup of $ X F^*(G)$ such that $X F^*(G)$ is quasinilpotent and $Y$ is a quasinilpotent subgroup of $N_G(X)$, then $Y F^*(N_G(X})$ is quasinilpotent if and only if $Y F^*(G)$ is quasinilpotent. Also we will obtain that $F^*{G}$ controls its own fusion in $G$ if and only if $G=F^*{G}$.
Group theory and generalizations
General
747
759
10.4171/RMI/335
http://www.ems-ph.org/doi/10.4171/RMI/335