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1.
Using isoperimetry we obtain new symmetrization inequalities that allow us to provide a unified framework to study Sobolev inequalities in metric spaces. The applications include concentration inequalities, Poincaré inequalities, as well as metric versions of the Pólya–Szegö and Faber–Krahn principles. To cite this article: J. Martín, M. Milman, C. R. Acad. Sci. Paris, Ser. I 347 (2009).  相似文献   

2.
Our aim in this paper is to deal with the boundedness of maximal functions in generalized Lebesgue spaces Lp(⋅) when p(⋅) satisfies a log-Hölder condition at infinity that is weaker than that of Cruz-Uribe, Fiorenza and Neugebauer [D. Cruz-Uribe, A. Fiorenza, C.J. Neugebauer, The maximal function on variable Lp spaces, Ann. Acad. Sci. Fenn. Math. 28 (2003) 223-238; 29 (2004) 247-249]. Our result extends the recent work of Diening [L. Diening, Maximal functions on generalized Lp(⋅) spaces, Math. Inequal. Appl. 7 (2004) 245-254] and the authors Futamura and Mizuta [T. Futamura, Y. Mizuta, Sobolev embeddings for Riesz potential space of variable exponent, preprint]. As an application of the boundedness of maximal functions, we show Sobolev's inequality for Riesz potentials with variable exponent.  相似文献   

3.
We study the solvability of a semilinear non-classical pseudodifferential boundary value problem in the Sobolev spaces Hl,p,q, 1<p<∞, depending on a complex parameter q. To cite this article: Y.V. Egorov et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).  相似文献   

4.
We establish sufficient conditions for the existence of solutions to a class of nonlinear eigenvalue problems involving nonhomogeneous differential operators in Orlicz–Sobolev spaces. To cite this article: M. Mih?ilescu et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).  相似文献   

5.
We use Young’s functions to define the Korenblum-Orlicz spaces as a generalization of the Korenblum spaces and we establish some of its properties. We show that the norm of the conformal maps in Korenblum-Orlicz spaces can be dominated by a certain expression involving the supremum over the inverse image of certain sectors. This extend a result of J. Ramos Fernández in (C. R. Math. Acad. Sci. Paris, 344(5):291–294, 2007) for α-Bloch spaces.  相似文献   

6.
ABSTRACT

The aim of this note is to survey recent results contained in Nguyen H-M, Squassina M. [On anisotropic Sobolev spaces. Commun Contemp Math, to appear. DOI:10.1142/S0219199718500177]; Nguyen H-M, Pinamonti A, Squassina M, et al. [New characterizations of magnetic Sobolev spaces. Adv Nonlinear Anal. 2018;7(2):227–245]; Pinamonti A, Squassina M, Vecchi E. [Magnetic BV functions and the Bourgain-Brezis-Mironescu formula. Adv Calc Var, to appear. DOI:10.1515/acv-2017-0019]; Pinamonti A, Squassina M, Vecchi E. [The Maz'ya-Shaposhnikova limit in the magnetic setting. J Math Anal Appl. 2017;449:1152–1159] and Squassina M, Volzone B. [Bourgain-Brezis-Mironescu formula for magnetic operators. C R Math Acad Sci Paris. 2016;354:825–831], where the authors extended to the magnetic setting several characterizations of Sobolev and BV functions.  相似文献   

7.
Among all W-spaces (i.e. spaces with nonvanishing Wronskians), extended Cheyshev spaces can be characterised by the existence of either Bernstein bases, or B-spline bases, or Bézier points, or blossoms in the spaces obtained by integration. To cite this article: M.-L. Mazure, C. R. Acad. Sci. Paris, Ser. I 339 (2004).  相似文献   

8.
9.
We identify the optimal range of coefficients s, p for which differential forms with coefficients in the Sobolev space Lps(Ω) admit natural Hodge decompositions in arbitrary two and three dimensional Lipschitz domains Ω. To cite this article: D. Mitrea, M. Mitrea, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 109–112  相似文献   

10.
We prove some new properties of the small Lebesgue spaces introduced by Fiorenza [7]. Combining these properties with the Poincaré–Sobolev inequalities for the relative rearrangement (see [11]), we derive some new and precises estimates either for small Lebesgue–Sobolev spaces or for quasilinear equations with data in the small Lebesgue spaces. To cite this article: A. Fiorenza, J.-M. Rakotoson, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 23–26  相似文献   

11.
Quasi-invariance under translation is established for the σ-finite measure unifying Brownian penalisations, which has been introduced by Najnudel, Roynette and Yor [J. Najnudel, B. Roynette, M. Yor, A remarkable σ-finite measure on C(R+,R) related to many Brownian penalisations, C. R. Math. Acad. Sci. Paris 345 (8) (2007) 459-466]. For this purpose, the theory of Wiener integrals for centered Bessel processes, due to Funaki, Hariya and Yor [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered Bessel and related processes. II, ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006) 225-240 (electronic)], plays a key role.  相似文献   

12.
13.
《Comptes Rendus Mathematique》2008,346(21-22):1123-1128
In their book Rapoport and Zink constructed rigid analytic period spaces for Fontaine's filtered isocrystals, and period morphisms from moduli spaces of p-divisible groups to some of these period spaces. We determine the image of these period morphisms, thereby contributing to a question of Grothendieck. We give examples showing that only in rare cases the image is all of the Rapoport–Zink period space. To cite this article: U. Hartl, C. R. Acad. Sci. Paris, Ser. I 346 (2008).  相似文献   

14.
In [C. Amrouche, V. Girault, J. Giroire, Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator. An approach in weighted Sobolev spaces, J. Math. Pures Appl. 76 (1997) 55-81], authors study Dirichlet and Neumann problems for the Laplace operator in exterior domains of Rn. This paper extends this study to the resolution of a mixed exterior Laplace's problem. Here, we give existence, unicity and regularity results in Lp's theory with 1<p<∞, in weighted Sobolev spaces.  相似文献   

15.
We study here the nonhomogeneous Neumann problem in the half-space RN+ with N?2. We give in Lp theory, with 1<p<∞, a basic existence and regularity results in weighted Sobolev spaces. To cite this article: C. Amrouche, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 151–156.  相似文献   

16.
《Comptes Rendus Mathematique》2008,346(23-24):1231-1234
In this Note, we establish sharp weighted Hardy type inequalities with a more general index p on polarizable Carnot groups, which include Kombe's recent results; then a weighted Hardy–Sobolev type inequality is obtained by using previous inequalities. To cite this article: J. Wang, P. Niu, C. R. Acad. Sci. Paris, Ser. I 346 (2008).  相似文献   

17.
We show that the cohomology groups of the Drinfeld symmetric space Ω(n+1) defined over a local field of any characteristic are GLn+1-isomorphic to certain spaces of harmonic cochains on the Bruhat–Tits building. To cite this article: Y. Aït Amrane, C. R. Acad. Sci. Paris, Ser. I 338 (2004).  相似文献   

18.
In this Note we prove the following result. A fine log scheme over the complex numbers and its saturated have homeomorphic Kato–Nakayama associated spaces. Moreover these spaces are isomorphic as ringed spaces, either with the ring sheaf defined by Kato–Nakayama, or with that defined by Ogus. In the definition of these spaces, non-integral monoids are involved, so that the proof of the result is based on properties of nonnecessarily integral monoids. To cite this article: M. Cailotto, C. R. Acad. Sci. Paris, Ser. I 339 (2004).  相似文献   

19.
In this Note, we give two applications to our work [Bayad, C. R. Acad. Sci. Paris, Ser. I 339 (2004); DOI: 10.1016/j.crma.2004.07.018] concerning multiple elliptic Apostol–Dedekind–Zagier sums. These elliptic sums are defined by means of certain Jacobi modular forms of two variables Dτ(z;φ). When Im(τ), these elliptic sums give the classical Apostol–Dedekind–Zagier multiple sums [Apostol, Duke Math. J. 17 (1950) 147–157, Pacific. J. Math 2 (1952) 1–9; Zagier, Math. Ann, 202 (1973) 149–172]. We give a reciprocity law for these sums. To cite this article: A. Bayad, C. R. Acad. Sci. Paris, Ser. I 339 (2004).  相似文献   

20.
It is known from differential geometry that one can reconstruct a curve with n?1 prescribed curvature functions, if these functions can be differentiated a certain number of times in the usual sense and if the first n?2 functions are strictly positive. We establish here that this result still holds under the assumption that the curvature functions belong to some Sobolev spaces, by using the notion of derivative in the distributional sense. We also show that the mapping that associates with such prescribed curvature functions the reconstructed curve is of class C. To cite this article: M. Szopos, C. R. Acad. Sci. Paris, Ser. I 338 (2004).  相似文献   

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