- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 15:43:53
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RMI&vol=9&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)
9
1993
2
Complex tangential characterizations of Hardy-Sobolev Spaces of holomorphic functions
Sandrine
Grellier
Université Paris-Sud, ORSAY CEDEX, FRANCE
General
201
255
10.4171/RMI/135
http://www.ems-ph.org/doi/10.4171/RMI/135
Wiener-Hopf integral operators with $PC$ symbols on spaces with Muckenhoupt weight
Albrecht
Böttcher
Technische Universität Chemnitz, CHEMNITZ, GERMANY
Ilya
Spitkovsky
The College of William and Mary, WILLIAMSBURG, UNITED STATES
We describe the spectrum and the essential spectrum and give an index formula for Wiener-Hopf integral operators with piecewise continuous symbols on the space $L^P (\mathbb R_+, \omega)$ with a Muckenhoupt weight $\omega$. Our main result says that the essential spectrum is a set resulting from the essential range of the symbol by joining the two endpoints of each jump by a certain sickle-shaped domain, whose shape is completely determined by the value of $p$ and the behavior of the weight $\omega$ at the origin and at infinity.
General
257
279
10.4171/RMI/136
http://www.ems-ph.org/doi/10.4171/RMI/136
Interpolation between $H^p$ Spaces and non-commutative generalizations, II
Gilles
Pisier
Texas A&M University, COLLEGE STATION, UNITED STATES
We continue an investigation started in a preceding paper. We discuss the classical results of Carleson connecting Carleson measures with the $\bar{\partial}$-equation in a slightly more abstract framework than usual. We also consider a more recent result of Peter Jones which shows the existence of a solution of the $\bar{\partial}$-equation, which satisfies simultaneously a good $L_\infty$ estimate and a good $L_1$ estimate. This appears as a special case of our main result which can be stated as follows: Let $(\Omega, \mathcal A, \mu)$ be any measure space. Consider a bounded operator $u : H^1 \rightarrow L_1(\mu)$. Assume that on one hand $u$ admits an extension $u_1 : L^1 \rightarrow L_1(\mu)$ bounded with norm $C_1$, and on the other hand that $u$ admits an extension $u_\infty : L^\infty \rightarrow L_\infty(\mu)$ bounded with norm $C_\infty$. Then $u$ admits an extension $\tilde{u}$ which is bounded simultaneously from $L^1$ into $L_1(\mu)$ and from $L^\infty$ into $L_\infty(\mu)$ and satisfies $$\| \tilde{u}: L_\infty \rightarrow L_\infty(\mu) \| ≤ C C_\infty$$ $$\| \tilde{u}: L_1 \rightarrow L_1 (\mu) \| ≤ C C_1$$ where $C$ is a numerical constant.
General
281
291
10.4171/RMI/137
http://www.ems-ph.org/doi/10.4171/RMI/137
Isopérimétrie pour les groupes et les variétés
Thierry
Coulhon
Université de Cergy-Pontoise, CERGY-PONTOISE CEDEX, FRANCE
Laurent
Saloff-Coste
Cornell University, ITHACA, UNITED STATES
General
293
314
10.4171/RMI/138
http://www.ems-ph.org/doi/10.4171/RMI/138
Initial traces of solutions to a one-phase Stefan problem in an infinite strip
Daniele
Andreucci
Università di Roma La Sapienza, ROMA, ITALY
M.
Korten
Universidad de Buenos Aires, BUENOS AIRES, ARGENTINA
General
315
332
10.4171/RMI/139
http://www.ems-ph.org/doi/10.4171/RMI/139
Ondelettes generalisées et fonctions d'échelle à support compact
Pierre Gilles
Lemarié-Rieusset
Université d'Évry Val d'Essonne, EVRY CEDEX, FRANCE
We show that to any multi-resolution analysis of $L^2 (\mathbb R)$ with multiplicity $d$, dilation factor $A$ (where $A$ is an integer ≥ 2) and with compactly supported scaling functions we may associate compactly supported wavelets. Conversely, if $\psi_{\epsilon, j, k} = A^{j/2}\psi_\epsilon (A^jx–k)), 1 ≤ \epsilon ≤ E, j, k \in \mathbb Z$ is a Hilbertian basis of $L^2 (\mathbb R)$ with continuous compactly supported mother functions $\psi_\epsilon$, then it is provided by a multi-resolution analysis with dilation factor $A$, multiplicity $d = E/(A–1)$ and with compactly supported scaling functions (which have the same regularity as the wavelets $\psi_\epsilon$). Those results can be extended to the cases of exponentially localized functions and of biorthogonal wavelets.
General
333
371
10.4171/RMI/140
http://www.ems-ph.org/doi/10.4171/RMI/140
Further pseudodifferential operators generating Feller semigroups and Dirichlet forms
Niels
Jacob
University of Wales Swansea, SWANSEA, UNITED KINGDOM
We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yosida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.
General
373
407
10.4171/RMI/141
http://www.ems-ph.org/doi/10.4171/RMI/141