We derive lower bounds for Lp norms
, in the central limit theorem for independent and m–dependent random variables with finite fifth order absolute moments and for independent and m–dependent identically distributed random variables with fourth order moments. 相似文献
Let be the Weinstein operator on the half space, . Suppose there is a sequence of Borel sets such that a certain tangential projection of onto forms a pairwise disjoint subset of the boundary. Let be a finite test measure on the boundary for a specific non-isotropic Hausdorff measure. The measure is carried back to a measure on a subset of by the projection. We give an upper bound for the Weinstein potential corresponding to the measure in terms of a universal constant and a Weinstein subharmonic function. We use this upper bound to deduce a result concerning tangential behavior of Weinstein potentials at the boundary with the exception of sets on the boundary of vanishing non-isotropic Hausdorff measure.
We prove the following theorem. Let m and n be any positive integers with mn, and let
be a subset of the n-dimensional Euclidean space n. For each i=1, . . . , m, there is a class
of subsets Mij
of Tn. Assume that
for each i=1, . . . , m, that M
ij
is nonempty and closed for all i, j, and that there exists a real number B(i, j) such that
and its jth component xjB(i, j) imply
. Then, there exists a partition
of {1, . . . , n} such that
for all i and
We prove this theorem based upon a generalization of a well-known theorem of Birkhoff and von Neumann. Moreover, we apply this theorem to the fair allocation problem of indivisible objects with money and obtain an existence theorem. 相似文献
We call a sequence (Tn) of measure preserving transformations strongly mixing if
tends to P(A)P(B) for arbitrary measurable A, B. We investigate whether one can pass to a suitable subsequence
such that
almost surely for all (or "many") integrable f. 相似文献
The main result of this paper is the following theorem. Suppose thatτ(n) = ∑d|n l and the arithmetical functionF satisfies the following conditions:
1)
the functionF is multiplicative;
2)
ifF(n) = ∑d|nf(d), then there exists an α>0 such that the relationf(n)=O(n−α) holds asn→∞.
Then there exist constantsA1,A2, andA3 such that for any fixed \g3\s>0 the following relation holds:
. Moreover, if for any primep the inequality \vbf(p)\vb\s<1 holds and the functionF is strongly multiplicative, thenA1\s>0.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 429–438, September, 2000. 相似文献
The mapping version of Pöschel's theory on differentiable foliation structures of invariant tori is presented and the relevant estimates explicitly in terms of the diophantine constant and the nondegeneracy parameters of frequency maps are given. As a direct application of the main result, a generalization of Moser's small twist theorem to high dimensions is given. 相似文献
Let X and Y be locally compact Hausdorff spaces and T : C0(X) C0(Y) a ring homomorphism. We completely characterize such homomorphisms and show that if T is R-linear, then T is either C-linear or C-antilinear. In any case T is continuous and there is a continuous map : YX such that Tf = f o , fC0(X) (if T is C-linear) or
(if T is C-antilinear). Thus, extending a result of Mólnar, we also derive the general form of an isometry T.AMS Subject Classification (2000): primary 46J05, 46E25(deceased) Passed away on 24 May 1999. 相似文献