共查询到20条相似文献,搜索用时 31 毫秒
1.
In this note, the authors show the boundedness of the maximal commutators of Bocher-Riesz operator B
δ
and that of maximal commutator B
δ1*
b
generated by B
δ
and a Lipschitz function b mapping from M
p
q
(R
n
) into BMO space and also maps from M
p
q
(R
n
) into L
(β−n/q). 相似文献
2.
We study univalent holomorphic functions in the unit diskU = {z: |z| < 1} of the formf(z)=z+∑
n=2
∞
a
n
z
n
that satisfy the condition Re zf’(z)/f(z) > α with α∈ [0, 1) inU. Some integral means of such funcions are estimated. 相似文献
3.
Let M be a manifold of X = C
n
, A a small analytic disc attached to M, z
o
a point of A where A is tangent to M, z
1 another point of A where M extends to a germ of manifold M
1 with boundary M. We prove that CR functions on M which extend to M
1 at z
1 also extend at z
o
to a new manifold M
2. The directions M
1 and M
2 point to, are related by a sort of connection associated to A which is dual to the connection obtained by attaching 'partial analytic lifts' of A to the co-normal bundle to M in X. 相似文献
4.
The present paper establishes a complete result on approximation by rational functions with prescribed numerator degree in
L
pspaces for 1 < p < ∞ and proves that if f(x)∈L
p
[-1,1] changes sign exactly l times in (-1,1), then there exists r(x)∈R
n
l such that
where R
n
l indicates all rational functions whose denominators consist of polynomials of degree n and numerators polynomials of degree l, and C
p
, l,
b
is a positive constant depending only on p, l and b which relates to the distance among the sign change points of f(x) and will be given in §3.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
On a Class of Generalized Lacunary Difference Sequence Spaces Defined by Orlicz Functions 总被引:1,自引:0,他引:1
In this article we introduce the generalized lacunary difference sequence spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and [N_θ,M,Δ~m]_∞using m~(th)- difference.We study their properties like completeness,solidness,symmetricity.Also we obtain some inclusion relations involving the spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and[N_θ,M,Δ~m]_∞and the Cesàro summable and strongly Cesàro summable sequences. 相似文献
6.
Thomas Schott 《Mathematische Nachrichten》1998,189(1):221-242
In this paper we define weighted function spaces of type Bspq(u) and Fspq(u) on the Euclidean space IRn, where u is a weight function of at most exponential growth. In particular, u(x) = exp(±|χ|) is an admissible weight. We prove some basic properties of these spaces, such as completeness and density of the smooth functions. 相似文献
7.
Luis A. Caffarelli 《偏微分方程通讯》2013,38(3):391-414
Consider a function u defined on n , except, perhaps, on a closed set of potential singularities . Suppose that u solves the eikonal equation ‖Du‖ = 1 in the pointwise sense on n \, where Du denotes the gradient of u and ‖·‖ is a norm on n with the dual norm ‖·‖?. For a class of norms which includes the standard p-norms on n , 1 < p < ∞, we show that if has Hausdorff 1-measure zero and n ≥ 2, then u is either affine or a “cone function,” that is, a function of the form u(x) = a ± ‖x ? z‖?. 相似文献
8.
For two subsets W and V of a Banach space X, let Kn(W, V, X) denote the relative Kolmogorov n-width of W relative to V defined by Kn (W, V, X) := inf sup Ln f∈W g∈V∩Ln inf ‖f-g‖x,where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2(△r) denote the class of 2w-periodic functions f with d-variables satisfying ∫[-π,π]d |△rf(x)|2dx ≤ 1,while △r is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2(△r) relative to W2(△r) in Lq([-r, πr]d) (1 ≤ q ≤∞), and obtain its weak asymptotic result. 相似文献
9.
G. R. Wood 《Journal of Optimization Theory and Applications》1988,58(2):331-350
A two-dimensional analogue of the well-known bisection method for root finding is presented in order to solve the following problem, related to the dispersion function of a set of random variables: given distribution functionsF
1,...,F
n and a probabilityp, find an interval [a,b] of minimum width such thatF
i(b)–F
i(a
–)p, fori=1,...,n.The author wishes to thank Dr. I. D. Coope, for helpful advice offered during the preparation of this paper, and the referee, whose comments contributed to a clearer presentation. 相似文献
10.
If X1, …, Xn are independent Rd-valued random vectors with common distribution function F, and if Fn is the empirical distribution function for X1, …, Xn, then, among other things, it is shown that P{supx Fn(x) ε} 2e2(2n)de−2nε2 for all nε2 ≥ d2. The inequality remains valid if the Xi are not identically distributed and F(x) is replaced by ΣiP{Xi ≤ x}/n. 相似文献
11.
Ming-Huat Lim 《Linear and Multilinear Algebra》2013,61(4):481-496
Let A be a non-empty set and m be a positive integer. Let ≡ be the equivalence relation defined on A m such that (x 1, …, x m ) ≡ (y 1, …, y m ) if there exists a permutation σ on {1, …, m} such that y σ(i) = x i for all i. Let A (m) denote the set of all equivalence classes determined by ≡. Two elements X and Y in A (m) are said to be adjacent if (x 1, …, x m?1, a) ∈ X and (x 1, …, x m?1, b) ∈ Y for some x 1, …, x m?1 ∈ A and some distinct elements a, b ∈ A. We study the structure of functions from A (m) to B (n) that send adjacent elements to adjacent elements when A has at least n + 2 elements and its application to linear preservers of non-zero decomposable symmetric tensors. 相似文献
12.
Charles B. Roosen Trevor J. Hastie 《Journal of computational and graphical statistics》2013,22(3):235-248
Abstract A highly flexible nonparametric regression model for predicting a response y given covariates {xk}d k=1 is the projection pursuit regression (PPR) model ? = h(x) = β0 + Σjβjfj(αT jx) where the fj , are general smooth functions with mean 0 and norm 1, and Σd k=1α2 kj=1. The standard PPR algorithm of Friedman and Stuetzle (1981) estimates the smooth functions fj using the supersmoother nonparametric scatterplot smoother. Friedman's algorithm constructs a model with M max linear combinations, then prunes back to a simpler model of size M ≤ M max, where M and M max are specified by the user. This article discusses an alternative algorithm in which the smooth functions are estimated using smoothing splines. The direction coefficients αj, the amount of smoothing in each direction, and the number of terms M and M max are determined to optimize a single generalized cross-validation measure. 相似文献
13.
Let L be a linear operator in L2(Rn) and generate an analytic semigroup {e-tL}t 0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0, ∞) be of upper type 1 and of critical lower type p0(ω) ∈ (n/(n + θ(L)), 1] and ρ(t) = t-1/ω-1(t-1) for t ∈ (0, ∞). We introduce the Orlicz-Hardy space Hω, L(Rn) and the BMO-type space BMOρ, L(Rn) and establish the John-Nirenberg inequality for BMOρ, L(Rn) functions and the duality relation between Hω, L(Rn) and BMOρ, L... 相似文献
14.
Let L be the infinitesimal generator of an analytic semigroup on L2(?n ) with Gaussian kernel bound, and let L–α /2 be the fractional integral of L for 0 < α < n. Suppose that b = (b1, b2, …, bm ) is a finite family of locally integral functions, then the multilinear commutator generated by b and L–α /2 is defined by L–α /2 b f = [bm , …, [b2, [b1, L–α /2]], …, ] f, where m ∈ ?+. When b1, b2, …, bm ∈ BMO or bj ∈ Λ (0 < βj < 1) for 1 ≤ j ≤ m, the authors study the boundedness of L–α /2 b . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Let σb(n) ≔ Σd|ndb. For every integer r ≥ 2 and for 0 < a < 1 we estabish an asymptotic estimate of Σn ≤ xσr–a(n). 相似文献
16.
S. N. Kudryavtsev 《Mathematical Notes》2005,77(3-4):494-498
We describe the weak asymptotics of the behavior of the Kolmogorov, Gelfand, linear, Aleksandrov, and entropy widths of the unit ball of the space W
p
l
Hw (I
d) in the space W
q
m
(I
d).Translated from Matematicheskie Zametki, vol. 77, no. 4, 2005, pp. 535–539.Original Russian Text Copyright © 2005 by S. N. Kudryavtsev.This revised version was published online in April 2005 with a corrected issue number. 相似文献
17.
For partial linear model Y = Xτβ0 g0(T) with unknown β0 ∈ Rd and an unknown smooth function g0, this paper considers the Huber-Dutter estimators of β0, scale σ for the errors and the function g0 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β0 and σ are shown to be asymptotically normal with the rate of convergence n-1/2 and the B-spline Huber-Dutter estimator of g0 achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of β0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. 相似文献
18.
Let S be a locally compact semigroup, let ω be a weight function on S, and let Ma (S, ω) be the weighted semigroup algebra of S. Let L∞0 (S;Ma (S, ω)) be the C*‐algebra of allMa (S, ω)‐measurable functions g on S such that g /ω vanishes at infinity. We introduce and study an Arens multiplication on L∞0 (S;Ma (S, ω))* under which Ma (S, ω) is a closed ideal. We show that the weighted measure algebra M (S, ω) plays an important role in the structure of L∞0 (S;Ma (S, ω))*. We then study Arens regularity of L∞0 (S;Ma (S, ω))* and ist relation with Arens regularity of Ma (S, ω), M (S, ω) and the discrete convolution algebra ℓ1(S, ω). As the main result, we prove that L∞0 (S;Ma (S, ω))* is Arens regular if and only if S is finite, or S is discrete and Ω is zero cluster. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
V. V. Karachik 《Siberian Advances in Mathematics》2008,18(2):103-117
Let u(x) be a function analytic in some neighborhood D about the origin, $ \mathcal{D} Let u(x) be a function analytic in some neighborhood D about the origin, ⊂ ℝ
n
. We study the representation of this function in the form of a series u(x) = u
0(x) + |x|2
u
1(x) + |x|4
u
2(x) + …, where u
k
(x) are functions harmonic in . This representation is a generalization of the well-known Almansi formula.
Original Russian Text ? V. V. Karachik, 2007, published in Matematicheskie Trudy, 2007, Vol. 10, No. 2, pp. 142–162. 相似文献
20.
This paper deals with atomic decompositions in spaces of type Bsp,q (?n , w), Fsp,q (?n , w), 0 < p < ∞, 0 < q ≤ ∞, s ∈ ?, where the weight function w belongs to some Muckenhoupt class Ar. In particular, we consider the weight function wΓκ (x) = dist(x, Γ)κ, where Γ is some d ‐set, 0 < d < n, and κ > –(n – d). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献