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1.
Let
be the Fejér kernel, C be the space of contiuous 2π-periodic functions f with the norm , let
be the Jackson polynomials of the function f, and let
be the Fejér sums of f. The paper presents upper bounds for certain quantities like
which are exact in order for every function f ∈ C. Special attention is paid to the constants occurring in the inequalities obtained. Bibliography: 14 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 90–114.  相似文献   

2.
We prove that
where X is a normal random element in the space C [0,1], MX = 0, σ = {(M|X(t)|2)1/2 t∈[0,1}, (X n ) are independent copies of X, and . Under additional restrictions on the random element X, this equality can be strengthened. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1227–1235, September, 1998.  相似文献   

3.
We show that a Banach space valued random variableX such that t} \right\} = 0$$ " align="middle" border="0"> satisfies the central limit theorem if and only if the following criterion on small balls is fulfilled:
t} \right\} = 0$$ " align="middle" vspace="20%" border="0">  相似文献   

4.
We prove the existence of continuously differentiable solutions such that
or
where
  相似文献   

5.
Let Sn = X1 + · · · + X n , n ≥ 1, and S 0 = 0, where X 1, X 2, . . . are independent, identically distributed random variables such that the distribution of S n/B n converges weakly to a nondeoenerate distribution F α as n → ∞ for some positive B n . We study asymptotic behavior of sums of the form
where
a function d(t) is continuous at [0,1] and has power decay at zero,
Bibliography: 13 titles. Translated from Zapiski Nauchnylch Serninarov POMI, Vol. 361, 2008, pp. 109–122.  相似文献   

6.
Let = (1,...,d) be a vector with positive components and let D be the corresponding mixed derivative (of order j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that
and
for all Moreover, if is the least possible value of the exponent in this inequality, then
Deceased.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 579–594, May, 2004.  相似文献   

7.
We obtain the new exact Kolmogorov-type inequality
for 2-periodic functions and any k, r N, k < r. We present applications of this inequality to problems of approximation of one class of functions by another class and estimates of K-functional type.  相似文献   

8.
We extend the results of Rubio de Francia and Bourgain by showing that, for arbitrary mutually disjoint intervals Δk ⊂ ℤ+, arbitrary p ∈, (0, 2], and arbitrary trigonometric polynomials f k with supp , we have
. The method is a development of that by Rubio de Francia. Bibliography: 9 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 98–114.  相似文献   

9.
For functions satisfying the boundary conditions
, the following inequality with sharp constants in additive form is proved:
wheren≥2, 0≤1≤n−2,−1≤m≤1, m+1≤n−3, and1≤p,q,r≤∞. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 712–724, November, 1997. Translated by N. K. Kulman  相似文献   

10.
We prove the following statement. Let , and let . Suppose that, for all and , the sequence satisfies the relation
where e(u) : = e2πiu . Then
where q is the set of q-multiplicative functions g such that .  相似文献   

11.
Let X, Y be vector spaces. It is shown that if a mapping f ： X → Y satisfies f（（x＋y）/2＋z）＋f（（x-y）/2＋z=f（x）＋2f（z）,（0.1） f（（x＋y）/2＋z）-f（（x-y）/2＋z）f（y）,（0.2） or 2f（（x＋y）/2＋x）=f（x）＋f（y）＋2f（z）（0.3）for all x, y, z ∈ X, then the mapping f ： X →Y is Cauchy additive. Furthermore, we prove the Cauchy-Rassias stability of the functional equations （0.1）, （0.2） and （0.3） in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras.  相似文献   

12.
Let be the space of 2-periodic functions whose (r – 1)th-order derivative is absolutely continuous on any segment and rth-order derivative belongs to L p, S 2n,m is the space of 2-periodic splines of order m of minimal defect over the uniform partition . In this paper, we construct linear operators such that
where
To construct the operators X n,r,m, we use the same idea as in the polynomial case, i.e., the interpolation of Bernoulli kernels. As is proved, the operators X n,r,m converge to polynomial Akhiezer–Krein–Favard operators as . Bibliography: 10 titles.  相似文献   

13.
We obtain a strengthened version of the Kolmogorov comparison theorem. In particular, this enables us to obtain a strengthened Kolmogorov inequality for functions x L x (r), namely,
where
k, r N, k < r, and r is a perfect Euler spline of order r. Using this inequality, we strengthen the Bernstein inequality for trigonometric polynomials and the Tikhomirov inequality for splines. Some other applications of this inequality are also given.  相似文献   

14.
We present a norm estimate for the partial transpose map Θ on the tensor product
with respect to a unitarily invariant norm. This is related to the norm estimates of the following maps on Mm,n in terms of the spectral norm of :
We show further that in the special case of as well as AX + XB and AX + XBT those estimates are much improved and that
for certain Schatten p-norms. Dedicated to the memory of late Professor Helmut H. Schaefer  相似文献   

15.
Let 1 < r < 2 and let b is a weight on ℝ such that satisfies the Muckenhoupt condition Ar′/2 (r′ is the exponent conjugate to r). If fj are functions whose Fourier transforms are supported on mutually disjoint intervals, then
for 0 < p ≤ r. Bibliography: 9 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 355, 2008, pp. 180–198.  相似文献   

16.
  相似文献   

17.
For functionsf which have an absolute continuous (n–1)th derivative on the interval [0, 1], it is proved that, in the case ofn>4, the inequality
  相似文献   

18.
This article is a continuation of [J. Math. Sci., 99, No.5, 1541–1547 (2000)] devoted to the validity of the Lax formula (cited in the article of Crandall, Ishii, and Lions [Bull. AMS, 27, No.1, 1–67 (2000)])
for a solution to the Hamilton–Jacobi nonlinear partial differential equation
where the Cauchy data are now a function semicontinuous from below, is the usual norm in , , and is a positive evolution parameter. We proved that the Lax formula solves the Cauchy problem (2) at all points , fixed save for an exceptional set of points R of the F type, having zero Lebesgue measure. In addition, we formulate a similar Lax-type formula without proof for a solution to a new nonlinear equation of the Hamilton–Jacobi-type:
where is a diagonal positive-definite matrix, mentioned in Part I and having interesting applications in modern mathematical physics.  相似文献   

19.
Let X be a Banach space and let (ξj)j ≧ 1 be an i.i.d. sequence of symmetric random variables with finite moments of all orders. We prove that the following assertions are equivalent:
1.  There exists a constant K such that
for all Lipschitz functions f : X → X satisfying f (0) = 0 and all finite sequences x1, ..., xn in X.
2.  X is isomorphic to a Hilbert space.
Received: 10 January 2005; revised: 5 April 2005  相似文献   

20.
Defant  Andreas 《Positivity》2001,5(2):153-175
The Maurey–Rosenthal theorem states that each bounded and linear operator T from a quasi normed space E into some Lp()(0) which satisfies a vector-valued norm inequality
even allows a weighted norm inequality: there is a function 0wL 0() such that
Continuing the work of Garcia-Cuerva and Rubio de Francia we give several scalar and vector-valued variants of this fundamental result within the framework of quasi Köthe function spaces X() over measure spaces. They are all special cases of our main result (Theorem 2) which extends the Maurey–Rosenthal cycle of ideas to the case of homogeneous operators between vector spaces being homogeneously representable in quasi Köthe function spaces.  相似文献   

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