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1.
We study optimal Hölder type inequalities for the Lorentz spaces L p,s (R, μ), in the range 1 < p < ∞, 1 ≤ s ≤ ∞, for both the maximal and the dual norms. These estimates also give sharp results for the corresponding associate norms.  相似文献   

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Zhao  Jianguo  Wu  Junliang 《Positivity》2017,21(4):1495-1506

The aim of this work is to present some Hölder-type inequalities for sums and products of operators related to unitarily invariant norms. These results generalize some known Hölder inequalities for operators.

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Using the Borwein–Preiss variational principle and in terms of the proximal coderivative, we provide a new type of sufficient conditions for the Hölder metric subregularity and Hölder error bounds in a class of smooth Banach spaces. As an application, new characterizations for the tilt stability of Hölder minimizers are established.  相似文献   

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Generalizations of the classic Grüss inequality in normed spaces are given. The results are illustrated with some specific examples.  相似文献   

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We prove Hölder type inequalities for integrals and conditional expectations involving the infinite product. Moreover, a generalized Doob maximal operator is introduced and weighted inequalities for this operator are established.  相似文献   

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A differential operator ?, arising from the differential expression $$lv(t) \equiv ( - 1)^r v^{[n]} (t) + \sum\nolimits_{k = 0}^{n - 1} {p_k } (t)v^{[k]} (t) + Av(t),0 \leqslant t \leqslant 1,$$ , and system of boundary value conditions $$P_v [v] = \sum\nolimits_{k = 0}^{n_v } {\alpha _{vk} } r^{[k]} (1) = 0.v - 1, \ldots ,\mu ,0 \leqslant \mu< n$$ is considered in a Banach space E. Herev [k](t)=(a(t) d/dt) k v(t)a(t) being continuous fort?0, α(t) >0 for t > 0 and \(\int_0^1 {\frac{{dz}}{{a(z)}} = + \infty ;}\) the operator A is strongly positive in E. The estimates , are obtained for ?: n even, λ varying over a half plane.  相似文献   

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We establish the equiconvergence of expansions of an arbitrary function in the class L 2(0, π) in the Fourier series in sines and in the Fourier series in the eigenfunctions of the first boundary value problem for the one-dimensional Schrödinger operator with a nonclassical potential. The equiconvergence is studied in the norm of the Hölder space. The potential is the derivative of a function that belongs to a fractional-order Sobolev space.  相似文献   

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We study the isometric extension problem for Hölder maps from subsets of any Banach space intoc 0 or into a space of continuous functions. For a Banach spaceX, we prove that anyα-Hölder map, with 0<α ≤1, from a subset ofX intoc 0 can be isometrically extended toX if and only ifX is finite dimensional. For a finite dimensional normed spaceX and for a compact metric spaceK, we prove that the set ofα’s for which allα-Hölder maps from a subset ofX intoC(K) can be extended isometrically is either (0, 1] or (0, 1) and we give examples of both occurrences. We also prove that for any metric spaceX, the above described set ofα’s does not depend onK, but only on finiteness ofK.  相似文献   

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It is proved that a functionuL m,p (R n ) (which coincides with the Sobolev spaceW 1,p (R n ) ifm=1) coincides with a Hölder continuous functionw outside a set of smallm,q-capacity, whereq<p. Moreover, ifm=1, then the functionw can be chosen to be close tou in theW 1,p -norm.  相似文献   

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Some inequalities for continuous synchronous (asynchronous) functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved operators, are given.  相似文献   

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Aequationes mathematicae - In this paper we study Grüss type inequalities for real and complex valued functions in probability spaces. Some earlier Grüss type inequalities are extended...  相似文献   

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For the step-weight function $\varphi \left( x \right) = \sqrt {1 - x^2 } $ , we prove that the Hölder spaces \gL{ina, p} on the interval [?1, 1], defined in terms of moduli of smoothness with the step-weight function ?, are linearly isomorphic to some sequence spaces, and the isomorphism is given by the coefficients of function with respect to a system of orthonormal splines with knots uniformly distributed according to the measure with density 1/?. In case \gL{ina, p} is contained in the space of continuous functions, we give a discrete characterization of this space, using only values of function at the appropriate knots. Application of these results to characterize the order of polynomial approximation is presented.  相似文献   

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In 1980, Yano showed that on smooth compact manifolds, for endomorphisms in dimension one or above and homeomorphisms in dimensions greater than one, topological entropy is generically infinite. It had earlier been shown that, for Lipschitz endomorphisms on such spaces, topological entropy is always finite. In this article, we investigate what occurs between C0-regularity and Lipschitz regularity, focussing on two cases: Hölder mappings and Sobolev mappings.  相似文献   

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Some trace operator inequalities for synchronous functions that are related to the ?eby?ev inequality for sequences of real numbers are given.  相似文献   

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Ouyang  Wei  Zhang  Binbin  Zhu  Jiangxing 《Positivity》2019,23(1):161-175
Positivity - This paper deals with the Hölder metric subregularity property of a certain constraint system in Asplund space. Using the techniques of variational analysis, its main part is...  相似文献   

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