共查询到20条相似文献,搜索用时 0 毫秒
1.
S. Thangavelu 《Journal of Functional Analysis》2007,251(2):438-462
Using Gutzmer's formula, due to Lassalle, we characterise the images of Sobolev spaces under the Segal-Bargmann transform on compact Riemannian symmetric spaces. We also obtain necessary and sufficient conditions on a holomorphic function to be in the image of smooth functions and distributions under the Segal-Bargmann transform. 相似文献
2.
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations. 相似文献
3.
We exhibit the optimal constant for Sobolev inequalities in Lorentz spaces for a mean oscillation, and its relation with a boundedness of the Hardy–Littlewood maximal operator in Sobolev spaces. Some applications to a scale invariant form of Hardy?s inequality in a limiting case are also considered. 相似文献
4.
Francesca Astengo Bianca Di Blasio 《Proceedings of the American Mathematical Society》2006,134(5):1319-1329
The generalised Cayley transform from an Iwasawa -group into the corresponding real unit sphere induces isomorphisms between suitable Sobolev spaces and . We study the differential of , and we obtain a criterion for a function to be in .
5.
In this paper, we pursue the study of harmonic functions on the real hyperbolic ball started in [13]. Our focus here is on the theory of Hardy‐Sobolev and Lipschitz spaces of these functions. We prove here that these spaces admit Fefferman‐Stein like characterizations in terms of maximal and square functionals. We further prove that the hyperbolic harmonic extension of Lipschitz functions on the boundary extend into Lipschitz functions on the whole ball. In doing so, we exhibit differences of behaviour of derivatives of harmonic functions depending on the parity of the dimension of the ball and on the parity of the order of derivation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen [2]. Our approach is based in the characterization of Lorentz spaces as real interpolation spaces. We will also study the sharpness and optimality of these inequalities. 相似文献
7.
《数学物理学报(A辑)》2003,23(1):106
该文讨论一类带有奇异系数的双重调和方程〖JB({〗△2u-μ[SX(]u[]|x|s[SX)]=f(x,u),\=u=[SX(]u[]ν[SX)]=0,〖JB)〗\ \ 〖JB(〗x∈Ω,x∈Ω,[JB)]
这里ΩRN是包含0的有界光滑区域,u∈H20(Ω),μ∈R是参数,0≤s≤2,△2=△△表示双重拉普拉斯算子.当f(x,u)=up,p=[SX(]2N[]N-4[SX)]时,上述问题就是一个临界双重调和问题. 该文运用Sobolev Hardy不等式和变分方法,得到它的解的存在性的一些结果. 相似文献
8.
《Journal of Approximation Theory》2003,120(2):185-216
The density of polynomials is straightforward to prove in Sobolev spaces Wk,p((a,b)), but there exist only partial results in weighted Sobolev spaces; here we improve some of these theorems. The situation is more complicated in infinite intervals, even for weighted Lp spaces; besides, in the present paper we have proved some other results for weighted Sobolev spaces in infinite intervals. 相似文献
9.
Wei-Shyan Tai 《Proceedings of the American Mathematical Society》2001,129(3):699-711
In this paper a capacitary weak type inequality for Sobolev functions is established and is applied to reprove some well-known results concerning Lebesgue points, Taylor expansions in the -sense, and the Lusin type approximation of Sobolev functions.
10.
Anatoly Ryabogin Dmitry Ryabogin 《Proceedings of the American Mathematical Society》2007,135(8):2461-2470
In this paper we give necessary and sufficient conditions for a harmonic vector and all its partial derivatives to belong to for all .
11.
12.
Simon P. Eveson Vladimir D. Stepanov Elena P. Ushakova 《Mathematische Nachrichten》2015,288(8-9):877-897
An embedding inequality of Sobolev type is characterized in the paper with help of a duality principle and boundedness criteria for the Hardy–Steklov integral operator in weighted Lebesgue spaces. 相似文献
13.
V. I. Chilin P. G. Dodds A. A. Sedaev F. A. Sukochev 《Transactions of the American Mathematical Society》1996,348(12):4895-4918
We present several characterizations of Kadec-Klee properties in symmetric function spaces on the half-line, based on the -functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respectively, local convergence in measure) on the unit sphere coincides with norm convergence.
14.
In this paper, we use a weighted version of Poincaré's inequality to study density and extension properties of weighted Sobolev spaces over some open set . Additionally, we study the specific case of monomial weights , showing the validity of a weighted Poincaré inequality together with some embedding properties of the associated weighed Sobolev spaces. 相似文献
15.
We investigate the spaces of functions on ?n for which the generalized partial derivatives Dequation/tex2gif-sup-2.gifkf exist and belong to different Lorentz spaces Lequation/tex2gif-sup-3.gif . For the functions in these spaces, the sharp estimates of the Besov type norms are found. The methods used in the paper are based on estimates of non‐increasing rearrangements. These methods enable us to cover also the case when some of the pk's are equal to 1. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
Pierre Bousquet Emmanuel Russ Yi Wang Po-Lam Yung 《Journal of Functional Analysis》2019,276(5):1430-1478
Let be an integer, and φ be a differential l-form on with coefficients. It was proved by Bourgain and Brezis ([5, Theorem 5]) that there exists a differential l-form ψ on with coefficients in such that . In the same work, Bourgain and Brezis also left as an open problem the extension of this result to the case of differential forms with coefficients in the higher order space or more generally in the fractional Sobolev spaces with . We give a positive answer to this question, provided that , where κ is the largest positive integer such that . The proof relies on an approximation result (interesting in its own right) for functions in by functions in , even though does not embed into in this critical case. The proofs rely on some techniques due to Bourgain and Brezis but the context of higher order and/or fractional Sobolev spaces creates various difficulties and requires new ideas and methods. 相似文献
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18.
Elvise Berchio Filippo Gazzola 《Journal of Mathematical Analysis and Applications》2006,320(2):718-735
By considering the kernels of the first two traces, four different second order Sobolev spaces may be constructed. For these spaces, embeddings into Lebesgue spaces, the best embedding constant and the possible existence of minimizers are studied. The Euler equation corresponding to some of these minimization problems is a semilinear biharmonic equation with boundary conditions involving third order derivatives: it is shown that the complementing condition is satisfied. 相似文献
19.
The Herz-type Sobolev spaces are introduced and the Sobolev theorem is established. The Herz-type Bessel potential spaces
and the relation between the Herz-type Sobolev spaces and Bessel potential spaces are discussed. As applications of these
theories, some regularity results of nonlinear quantities appearing in the compensated compactness theory on Herz-type Hardy
spaces are given.
Project supported by the National Natural Science Foundation of China. 相似文献
20.
Andrea Cianchi 《Journal of Mathematical Analysis and Applications》2003,282(1):128-150
Necessary and sufficient conditions on a rearrangement-invariant Banach function space X(Q) on a cube Q in , n?2, are given for the corresponding Sobolev space W1X(Q) to be continuously embedded into (generalized) Campanato, Morrey, or Hölder spaces. The optimal such r.i. spaces X(Q) are found. As a by-product, sharp inclusion relations are proved among Campanato, Morrey, and Hölder type spaces. 相似文献