共查询到20条相似文献,搜索用时 15 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.
3.
Denis A. Labutin 《Proceedings of the American Mathematical Society》2000,128(11):3399-3403
For an arbitrary open set we characterize all functions on the real line such that for all . New element in the proof is based on Maz'ya's capacitary criterion for the imbedding . 相似文献
4.
《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
5.
We characterize the domain of the Wiener integral with respect to the fractional Brownian motion of any Hurst parameter H(0,1) on an interval [0,T]. The domain is the set of restrictions to of the distributions of with support contained in [0,T]. In the case H1/2 any element of the domain is given by a function, but in the case H>1/2 this space contains distributions that are not given by functions. The techniques used in the proofs involve distribution theory and Fourier analysis, and allow to study simultaneously both cases H<1/2 and H>1/2. 相似文献
6.
We prove well-posedness results for the initial value problem of the periodic KdV equation as well as Kam type results in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential decay of Fourier coefficients, and ‘almost well posed’ in spaces with exponential decay of Fourier coefficients. 相似文献
7.
We characterize the real interpolation space between a weighted space and a weighted Sobolev space in arbitrary bounded domains in , with weights that are positive powers of the distance to the boundary. 相似文献
8.
Flows associated to adapted vector fields on the Wiener space 总被引:1,自引:0,他引:1
The existence and uniqueness of a flow associated to an adapted vector field ξ on the Wiener space with are proved by a modified Picard's iteration method, mainly under the conditions of exponential integrability concerning bα as well as the first-order Malliavin gradients of and bα. A Newton–Leibnitz type inequality for a kind of Malliavin differentiable functionals is also proved, which is the key point to prove the above result, and has an independent interest. 相似文献
9.
Wojciech M. Zaja̧czkowski 《Mathematical Methods in the Applied Sciences》2011,34(2):191-197
Let f∈L2, ? µ(?3), where where x = (x1, x2, x3) is the Cartesian system in ?3, x′ = (x1, x2), , µ∈?+\?. We prove the decomposition f = ? ?u + g, with g divergence free and u is a solution to the problem in ?3 Given f∈L2, ? µ(?3) we show the existence of u∈H(?3) such that where Since f, u, g are defined in ?3 we need a sufficiently fast decay of these functions as |x|→∞. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
10.
Germán Fonseca 《Journal of Functional Analysis》2011,260(2):436-459
We study the initial value problem associated to the Benjamin-Ono equation. The aim is to establish persistence properties of the solution flow in the weighted Sobolev spaces , s∈R, s?1 and s?r. We also prove some unique continuation properties of the solution flow in these spaces. In particular, these continuation principles demonstrate that our persistence properties are sharp. 相似文献
11.
Hannes Luiro 《Proceedings of the American Mathematical Society》2007,135(1):243-251
We establish the continuity of the Hardy-Littlewood maximal operator on Sobolev spaces , . As an auxiliary tool we prove an explicit formula for the derivative of the maximal function.
12.
《Expositiones Mathematicae》2020,38(4):480-495
The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure. 相似文献
13.
Béatrice Vedel 《Mathematische Nachrichten》2009,282(1):104-124
We present a construction of “flat wavelet bases” adapted to the homogeneous Sobolev spaces ?s (?n ). They solve the problem of the phenomenon of infrared divergence which appears for usual wavelet expansions in ?s (?n ): these bases remove the divergence in the case s – n /2 ? ? since they are also bases of the realization of ?s (?n ). In the critical case s – n /2 ∈ ?, they provide a confinement of the divergence in a “small” space. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
Tahar Z. Boulmezaoud 《Mathematical Methods in the Applied Sciences》2002,25(5):373-398
In this paper, we investigate the Stokes system and the biharmonic equation in a half‐space of ?n. Our approach rests on the use of a family of weighted Sobolev spaces as a framework for describing the behaviour at infinity. A complete class of existence, uniqueness and regularity results for both the problems is proved. The proofs are mainly based on the principle of reflection. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
15.
In this paper, we obtain inequalities involving the Taylor polynomial and weak derivatives of a function in an Orlicz–Sobolev type space. Moreover, we show that any such function can be expanded in a finite Taylor series almost everywhere. As a consequence, we prove that the coefficients of any extended best polynomial -approximation of a function on a ball almost everywhere converge to the weak derivatives of such a function when the radius tends to 0. Lastly, we get a mean convergence result of such coefficients. 相似文献
16.
David Swanson 《Proceedings of the American Mathematical Society》2002,130(6):1655-1659
We show how the Sobolev space may be characterized in terms of the local behavior of its members. We use the local -classes introduced by Calderón and Zygmund.
17.
We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillatorH = −δ+|x|2. Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence
of solutions of the Schrodinger equation are also considered. 相似文献
18.
Wojciech M. Zaja̧czkowski 《Mathematical Methods in the Applied Sciences》2011,34(5):544-562
We consider an initial‐boundary value problem for nonstationary Stokes system in a bounded domain Omega??3 with slip boundary conditions. We assume that Ω is crossed by an axis L. Let us introduce the following weighted Sobolev spaces with finite norms: and where ?(x) = dist{x, L}. We proved the result. Given the external force f∈L2, ?µ(ΩT), initial velocity v0∈H(Ω), µ∈?+\? there exist velocity v∈H(ΩT) and the pressure p, ?p∈L2, ?µ(ΩT) and a constant c, independent of v, p, f, such that As we consider the Stokes system in weighted Sobolev spaces the following two things must be used:
- 1. the slip boundary condition and
- 2. the Helmholtz–Weyl decomposition.
19.
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
20.
Rajula Srivastava 《Mathematische Nachrichten》2023,296(2):853-875
We exhibit the necessary range for which functions in the Sobolev spaces can be represented as an unconditional sum of orthonormal spline wavelet systems, such as the Battle–Lemarié wavelets. We also consider the natural extensions to Triebel–Lizorkin spaces. This builds upon, and is a generalization of, previous work of Seeger and Ullrich, where analogous results were established for the Haar wavelet system. 相似文献