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1.
Hölder's inequality states that for any with . In the same situation we prove the following stronger chains of inequalities, where : A similar result holds for complex valued functions with Re substituting for . We obtain these inequalities from some stronger (though slightly more involved) ones. 相似文献
2.
We derive a sharp uncertainty inequality of the form with . As a consequence of this inequality we derive an upper bound for the so-called Laue constant, that is, the infimum of the functional , taken over all with (). Precisely, we obtain that which improves a previous bound of T. Gneiting. 相似文献
3.
Let be real numbers with and Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . This inequality is called the Furuta inequality and has many applications. In this paper, we prove that the Furuta inequality holds in a unital hermitian Banach -algebra with continuous involution. 相似文献
4.
We show that every positive solution of the equation where , converges to a period two solution. 相似文献
5.
In this paper we consider the theta correspondence between the sets and when is a nonarchimedean local field and . Our main theorem determines all the elements of that occur in the correspondence. The answer involves distinguished representations. As a corollary, we characterize all the elements of that occur in the theta correspondence between and . We also apply our main result to prove a case of a new conjecture of S.S. Kudla concerning the first occurrence of a representation in the theta correspondence. 相似文献
6.
A collection of subsets of a space is minimal if each element of contains a point which is not contained in any other element of . A base of a topological space is -minimal if it can be written as a union of countably many minimal collections. We will construct a compact linearly ordered space satisfying that is not metrizable and every subspace of has a -minimal base for its relative topology. This answers a problem of Bennett and Lutzer in the negative. 相似文献
7.
Let with . We consider the equations with and . We show that if is a convex bounded region in , there exists at least one classical solution to this boundary value problem. If the region is not convex, we show the existence of a weak solution. Partial results for the existence of classical solutions for non-convex domains in are also given. 相似文献
8.
We study the Fourier expansion of a function in orthogonal polynomial series with respect to the weight functions on the standard simplex in . It is proved that such an expansion is uniformly summable on the simplex for any continuous function if and only if . Moreover, it is shown that means define a positive linear polynomial identity, and the index is sharp in the sense that means are not positive for . 相似文献
9.
Very recently, Furuta obtained the grand Furuta inequality which is a parameteric formula interpolating the Furuta inequality and the Ando-Hiai inequality as follows : If and is invertible, then for each , is a decreasing function of both and for all and . In this note, we employ a mean theoretic approach to the grand Furuta inequality. Consequently we propose a basic inequality, by which we present a simple proof of the grand Furuta inequality. 相似文献
10.
We consider the Hausdorff measures , , defined on with the topology induced by the metric for all . We study its properties, their relation to the ``Lebesgue measure" defined on by R. Baker in 1991, and the associated Hausdorff dimension. Finally, we give some examples. 相似文献
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