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On , n?1 and n≠2, we prove the existence of a sharp constant for Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. For n>2s and any function satisfies where the operator (?Δ)s in Fourier spaces is defined by . To cite this article: A. Cotsiolis, N.C. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 801–804. 相似文献
3.
Michel Coornaert Athanase Papadopoulos 《Transactions of the American Mathematical Society》1999,351(7):2745-2762
Let be a -space which is spherically symmetric around some point and whose boundary has finite positive dimensional Hausdorff measure. Let be a conformal density of dimension on . We prove that is a weak limit of measures supported on spheres centered at . These measures are expressed in terms of the total mass function of and of the dimensional spherical function on . In particular, this result proves that is entirely determined by its dimension and its total mass function. The results of this paper apply in particular for symmetric spaces of rank one and semi-homogeneous trees.
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On , we prove the existence of sharp logarithmic Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. Any function f ∈ satisfies with be any number and where the operators in Fourier spaces are defined by . To cite this article: A. Cotsiolis, N.K. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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Athanase Cotsiolis 《Journal of Mathematical Analysis and Applications》2004,295(1):225-236
We obtain sharp constants for Sobolev inequalities for higher order fractional derivatives. As an application, we give a new proof of a theorem of W. Beckner concerning conformally invariant higher-order differential operators on the sphere. 相似文献
7.
Lixin Liu Athanase Papadopoulos Weixu Su Guillaume Théret 《Monatshefte für Mathematik》2010,161(3):295-311
We consider some metrics and weak metrics defined on the Teichmüller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comparison is on subsets of Teichmüller space which we call “ε 0-relative \({\epsilon}\)-thick parts”, and whose definition depends on the choice of some positive constants ε 0 and \({\epsilon}\). Meanwhile, we give a formula for the Teichmüller metric of a surface with boundary in terms of extremal lengths of families of arcs. 相似文献
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This paper has two parts. In the first part, we study shift coordinates on a sphere S equipped with three distinguished points and a triangulation whose vertices are the distinguished points. These coordinates
parametrize a space
(S)\widetilde{{\cal T}}(S)
that we call an unfolded Teichmüller space. This space contains Teichmüller spaces of the sphere with
\frak b{\frak b}
boundary components and
\frak p{\frak p}
cusps (which we call generalized pairs of pants), for all possible values of
\frak b{\frak b}
and
\frak p{\frak p}
satisfying
\frak b+\frak p=3{\frak b}+{\frak p}=3
. The parametrization of
[(T)\tilde](S)\widetilde{{\cal T}}(S)
by shift coordinates equips this space with a natural polyhedral structure, which we describe more precisely as a cone over
an octahedron in
\Bbb R3{\Bbb {R}}^3
. Each cone over a simplex of this octahedron is interpreted as a Teichmüller space of the sphere with
\frak b{\frak b}
boundary components and
\frak p{\frak p}
cusps, for fixed
\frak b{\frak b}
and
\frak p{\frak p}
, the sphere being furthermore equipped with an orientation on each boundary component. There is a natural linear action of
a finite group on
[(T)\tilde](S)\widetilde{{\cal T}}(S)
whose quotient is an augmented Teichmüller space in the usual sense. We describe several aspects of the geometry of the space
[(T)\tilde](S)\widetilde{{\cal T}}(S)
. Stretch lines and earthquakes can be defined on this space. In the second part of the paper, we use the shift coordinates
to obtain estimates on the behaviour of stretch lines in the Teichmüller space of a surface obtained by gluing hyperbolic
pairs of pants. We also use the shift coordinates to give formulae that express stretch lines in terms of Fenchel-Nielsen
coordinates. We deduce the disjointness of some stretch lines in Teichmüller space. We study in more detail the case of a
closed surface of genus 2. 相似文献
9.
Jacques Muzart Franoise Hnin Jean-Pierre Pte Athanase M'Boungou-M'Passi 《Tetrahedron: Asymmetry》1993,4(12):2531-2534
From the study of the tautomerization of prochiral dienols photogenerated in an organic solvent between −76 and +30°C in the presence of optically active aminoalcohols and in using the methodology developed by Scharf's group, the isoinversion temperature of the asymmetric process has been estimated to be −55°C. 相似文献
10.
This paper has two parts. In the first part, we study shift coordinates on a sphere S equipped with three distinguished points and a triangulation whose vertices are the distinguished points. These coordinates
parametrize a space
that we call an unfolded Teichmüller space. This space contains Teichmüller spaces of the sphere with
boundary components and
cusps (which we call generalized pairs of pants), for all possible values of
and
satisfying
. The parametrization of
by shift coordinates equips this space with a natural polyhedral structure, which we describe more precisely as a cone over
an octahedron in
. Each cone over a simplex of this octahedron is interpreted as a Teichmüller space of the sphere with
boundary components and
cusps, for fixed
and
, the sphere being furthermore equipped with an orientation on each boundary component. There is a natural linear action of
a finite group on
whose quotient is an augmented Teichmüller space in the usual sense. We describe several aspects of the geometry of the space
. Stretch lines and earthquakes can be defined on this space. In the second part of the paper, we use the shift coordinates
to obtain estimates on the behaviour of stretch lines in the Teichmüller space of a surface obtained by gluing hyperbolic
pairs of pants. We also use the shift coordinates to give formulae that express stretch lines in terms of Fenchel-Nielsen
coordinates. We deduce the disjointness of some stretch lines in Teichmüller space. We study in more detail the case of a
closed surface of genus 2.
Authors’ addresses: A. Papadopoulos, Institut de Recherche Mathématique Avancée, Université Louis Pasteur and CNRS, 7 rue
René Descartes, 67084 Strasbourg Cedex, France and Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany;
G. Théret, Institut de Recherche Mathématique Avancée, Université Louis Pasteur and CNRS, 7 rue René Descartes, 67084 Strasbourg
Cedex, France and Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, Building 1530, DK-8000 Aarhus C,
Denmark 相似文献