共查询到20条相似文献,搜索用时 15 毫秒
1.
N.G. Samko S.G. Samko B.G. Vakulov 《Journal of Mathematical Analysis and Applications》2007,335(1):560-583
For the Riesz potential operator Iα there are proved weighted estimates
2.
We prove various generalizations of classical Sard's theorem to mappings f:M m →N n between manifolds in Hölder and Sobolev classes. It turns out that if f ∈ C k,λ (M m ,N n ), then—for arbitrary k and λ—one can obtain estimates of the Hausdorff measure of the set of critical points in a typical level set f ?1(y). The classical theorem of Sard holds true for f ∈ C k with sufficiently large k, i.e., k>max(m?n,0); our estimates contain Sard's theorem (and improvements due to Dubovitskii and Bates) as special cases. For Sobolev mappings between manifolds, we describe the structure of f ?1(y). 相似文献
3.
E. I. Berezhnoi 《Proceedings of the Steklov Institute of Mathematics》2014,284(1):32-49
A sharp correction theorem is established for Sobolev spaces in which the norm (quasinorm) of generalized derivatives is calculated in an arbitrary symmetric space. The exact relation between the norm of a corrected function in the Lipschitz space and the measure of the set on which the corrected and original functions are different makes it possible to characterize the Sobolev spaces constructed on the basis of the Marcinkiewicz space in terms of correctability. This opens a way to constructing Sobolev-Marcinkiewicz spaces for functions with an arbitrary domain of definition. 相似文献
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Julián Fernández Bonder Nicolas Saintier Analia Silva 《Journal of Differential Equations》2012,253(5):1604-1620
In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration–Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico. 相似文献
6.
This article is devoted to the investigation of some properties of Sobolev spaces with mixed norm.Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 62–72, January, 1996. 相似文献
7.
Zhonghai Ding 《Proceedings of the American Mathematical Society》1996,124(2):591-600
A complete proof of the trace theorem of Sobolev spaces on Lipschitz domains has not appeared in the literature yet. The purpose of this paper is to give a complete proof of the trace theorem of Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on . It is proved that the trace operator is a linear bounded operator from to for .
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9.
V. N. Demenko 《Mathematical Notes》2000,67(3):286-295
In the paper, we construct a system of smooth two-dimensional splines and describe a class of measures for which this system
is a basis in the Sobolev weight space on the square.
Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 343–354, March, 2000. 相似文献
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11.
S Poornima 《Journal of Functional Analysis》1982,45(1):1-28
Let Wm,p denote the Sobolev space of functions on n whose distributional derivatives of order up to m lie in Lp(n) for 1 ? p ? ∞. When 1 < p < ∞, it is known that the multipliers on Wm,p are the same as those on Lp. This result is true for p = 1 only if n = 1. For, we prove that the integrable distributions of order ?1 whose first order derivatives are also integrable of order ?1, belong to the class of multipliers on Wm,1 and there are such distributions which are not bounded measures. These distributions are also multipliers on Lp, for 1 < p < ∞. Moreover, they form exactly the multiplier space of a certain Segal algebra. We have also proved that the multipliers on Wm,l are necessarily integrable distributions of order ?1 or ?2 accordingly as m is odd or even. We have obtained the multipliers from L1(n) into Wm,p, 1 ? p ? ∞, and the multiplier space of Wm,1 is realised as a dual space of certain continuous functions on n which vanish at infinity. 相似文献
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13.
V. L. Vaskevich 《Siberian Mathematical Journal》2017,58(3):408-418
We study sequences of cubature formulas on the unit sphere in a multidimensional Euclidean space. The grids for the cubature formulas under consideration embed in each other consecutively, forming in the limit a dense subset on the initial sphere. As the domain of cubature formulas, i.e. as the class of integrands, we take spherical Sobolev spaces. These spaces may have fractional smoothness. We prove that, among all possible spherical cubature formulas with given grid, there exists and is unique a formula with the least norm of the error, an optimal formula. The weights of the optimal cubature formula are shown to be solutions to a special nondegenerate system of linear equations. We prove that the errors of cubature formulas tend to zero as the number of nodes grows indefinitely. 相似文献
14.
A new method for approximating functions by uniform B-splines is presented. It is based on the orthogonality relations for
uniform B-splines in weighted Sobolev spaces, as introduced in (Reif, 1997). The scheme is local and the approximation order
is optimal. Moreover, also constrained approximation problems can be solved efficiently; the size of the linear system to
be solved is given by the number of constraints. Applying the method to spline conversion problems specifies new weights for
knot removal and degree reduction.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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16.
N. O. Belova 《Mathematical Notes》1994,56(2):856-858
Translated from Matematicheskie Zametki, Vol. 56, No. 2, pp. 136–139, August, 1994. 相似文献
17.
Summary.
Numerical methods are considered for generating polynomials
orthogonal with respect to an inner product of Sobolev type, i.e.,
one that involves derivatives up to some given order, each
having its own (positive) measure associated with it. The principal
objective is to compute the coefficients in the increasing-order
recurrence relation that these polynomials satisfy by virtue of
them forming a sequence of monic polynomials with degrees increasing
by 1 from one member to the next. As a by-product of this computation,
one gains access to the zeros of these polynomials via eigenvalues of
an upper Hessenberg matrix formed by the coefficients generated. Two
methods are developed: One is based on the modified moments of the
constitutive measures and generalizes what for ordinary orthogonal
polynomials is known as "modified Chebyshev algorithm". The
other - a generalization of "Stieltjes's procedure" -
expresses the desired coefficients in terms of a Sobolev inner product
involving the orthogonal polynomials in question, whereby the inner
product is evaluated by numerical quadrature and the polynomials
involved are computed by means of the recurrence relation already
generated up to that point. The numerical characteristics of these
methods are illustrated in the case of Sobolev orthogonal polynomials
of old as well as new types. Based on extensive numerical
experimentation, a number of conjectures are formulated with regard
to the location and interlacing properties of the respective zeros.
Received July 13, 1994 /
Revised version received September 26, 1994 相似文献
18.
In this paper q-Sobolev type spaces are defined on Rq by using the q-cosine Fourier transform and its inverse. In particular, embedding results for these spaces are established. Next we define the q-cosine potential and study some of its properties. 相似文献
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20.
Jean Van Schaftingen 《Journal of Functional Analysis》2006,236(2):490-516
The function spaces Dk(Rn) are introduced and studied. The definition of these spaces is based on a regularity property for the critical Sobolev spaces Ws,p(Rn), where sp=n, obtained by J. Bourgain, H. Brezis, New estimates for the Laplacian, the div-curl, and related Hodge systems, C. R. Math. Acad. Sci. Paris 338 (7) (2004) 539-543 (see also J. Van Schaftingen, Estimates for L1-vector fields, C. R. Math. Acad. Sci. Paris 339 (3) (2004) 181-186). The spaces Dk(Rn) contain all the critical Sobolev spaces. They are embedded in BMO(Rn), but not in VMO(Rn). Moreover, they have some extension and trace properties that BMO(Rn) does not have. 相似文献