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1.
For a vector measure ν having values in a real or complex Banach space and \({p \in}\) [1, ∞), we consider L p (ν) and \({L_{w}^{p}(\nu)}\), the corresponding spaces of p-integrable and scalarly p-integrable functions. Given μ, a Rybakov measure for ν, and taking q to be the conjugate exponent of p, we construct a μ-Köthe function space E q (μ) and show it is σ-order continuous when p > 1. In this case, for the associate spaces we prove that L p (ν) ×  = E q (μ) and \({E_q(\mu)^\times = L_w^p(\nu)}\). It follows that \({L_p (\nu) ^{**} = L_w^p (\nu)}\). We also show that L 1 (ν) ×  may be equal or not to E (μ).  相似文献   

2.
In this article we study the problem of extending Fourier Multipliers on L p (T) to those on L p (R) by taking convolution with a kernel, called a summability kernel. We characterize the space of such kernels for the cases p = 1 and p = 2. For other values of p we give a necessary condition for a function to be a summability kernel. For the case p = 1, we present properties of measures which are transferred from M(T) to M(R) by summability kernels. Furthermore it is shown that every l p sequence can be extended to some L q (R) multipliers for certain values of p and q.  相似文献   

3.
In this paper Lambert multipliers acting between L p spaces are characterized by using some properties of conditional expectation operator. Also, Fredholmness of corresponding bounded operators is investigated.  相似文献   

4.
We give a characterization of structurally stable diffeomorphisms by making use of the notion of L p -shadowing property. More precisely, we prove that the set of structurally stable diffeomorphisms coincides with the C 1-interior of the set of diffeomorphisms having L p -shadowing property.  相似文献   

5.
In this paper, the Lp(Rn)-boundedness of the commutators generalized by BMO(Rn) function and the singular integral operator T with rough kernel Ω∈ Llog+ L(Sn-1) is proved by using the Bony's formula for the paraproduct of two functions.  相似文献   

6.
7.
A weighted norm inequality for the Marcinkiewicz integral operator is proved when belongs to . We also give the weighted Lp-boundedness for a class of Marcinkiewicz integral operators with rough kernels and related to the Littlewood-Paley -function and the area integral S, respectively.  相似文献   

8.
Functions whose translates span L p (R) are called L p-cyclic functions. For a fixed p \memb [1, \infty], we construct Schwartz-class functions which are L r -cyclic for r > p and not L r - cyclic for r \le p. We then construct Schwartz-class functions which are L r -cyclic for r \ge p and not L r -cyclic for r < p. The constructions differ for p \memb (1, 2) and p > 2.  相似文献   

9.
Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L 2 normalized family of functions such that P(h)u(h) is O(h) in L 2(M) as h↓0. Let HM be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L p norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator.  相似文献   

10.
In order to approximate functions defined on (0, +∞), the authors consider suitable Lagrange polynomials and show their convergence in weighted L p -spaces.   相似文献   

11.
In this paper we determine the lower and upper estimates for the essential norm of finite sum of weighted Frobenius-Perron and weighted composition operators on L p spaces under certain conditions.  相似文献   

12.
L p approximation capability of radial basis function (RBF) neural networks is investigated. If g: R +1R 1 and ∈ L loc p (R n ) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L p (K) with any accuracy for any compact set K in R n , if and only if g(x) is not an even polynomial. Partly supported by the National Natural Science Foundation of China (10471017)  相似文献   

13.
This paper deals with the L p -consistency of wavelet estimators for a density function based on size-biased random samples. More precisely, we firstly show the L p -consistency of wavelet estimators for independent and identically distributed random vectors in R d . Then a similar result is obtained for negatively associated samples under the additional assumptions d = 1 and the monotonicity of the weight function.  相似文献   

14.
We introduce the concept of Lp-maximal regularity for second order Cauchy problems. We prove Lp-maximal regularity for an abstract model problem and we apply the abstract results to prove existence, uniqueness and regularity of solutions for nonlinear wave equations. The author acknowledges with thanks the support provided by the Department ofApplied Analysis, University of Ulm, and the travel grants provided by NBMH India and MSF Delhi, India.  相似文献   

15.
Much of the recent literature on risk measures is concerned with essentially bounded risks in L . In this paper we investigate in detail continuity and representation properties of convex risk measures on L p spaces. This frame for risks is natural from the point of view of applications since risks are typically modelled by unbounded random variables. The various continuity properties of risk measures can be interpreted as robustness properties and are useful tools for approximations. As particular examples of risk measures on L p we discuss the expected shortfall and the shortfall risk. In the final part of the paper we consider the optimal risk allocation problem for L p risks.  相似文献   

16.
Let G be a locally compact group. For 1 < p < ∞, it is well-known that f * g exists and belongs to Lp(G) for all f, g Lp (G) if and only if G is compact. Here, for 2 < p < ∞, we show that f * g exists for all f, g Lp(G) if and only if G is compact. We also show that this result does not remain true for 1 < p ≤ 2. Received: 23 April 2006  相似文献   

17.
Let Γ ⊂ ℝn, n ≥ 2, be the boundary of a bounded domain. We prove that the translates by elements of Γ of functions which transform according to a fixed irreducible representation of the orthogonal group form a dense class in L p (ℝn) for . A similar problem for noncompact symmetric spaces of rank one is also considered. We also study the connection of the above problem with the injectivity sets for weighted spherical mean operators. The first author was supported in part by a grant from UGC via DSA-SAP Phase IV.  相似文献   

18.
Let G be a locally compact group, ω be a weight function on G and 1 < p < ∞. Here, we give a sufficient condition for that the weighted L p -space L p (G, ω) is a Banach algebra. Also, we get some necessary conditions on G and the weight function ω for L p (G, ω) to be a Banach algebra. As a consequence, we show that if G is abelian and L p (G, ω) is a Banach algebra, then G is σ-compact.  相似文献   

19.
We derive interior L p -estimates for solutions of linear elliptic systems with oscillatory coefficients. The estimates are independent of ε, the small length scale of the rapid oscillations. So far, such results are based on potential theory and restricted to periodic coefficients. Our approach relies on BMO-estimates and an interpolation argument, gradients are treated with the help of finite differences. This allows to treat coefficients that depend on a fast and a slow variable. The estimates imply an L p -corrector result for approximate solutions.   相似文献   

20.
Let G be a locally compact group, ω a weight function on G, and 1<p<∞. We introduce the Lebesgue weighted L p -space \({\mathcal{L}}_{\omega}^{1,p}(G)= L^{p}(G,\omega)\cap L^{1}(G)\) as a Banach space and introduce its dual. Furthermore, we consider this space as a Banach algebra with respect to the usual convolution and show that \({\mathcal{L}}_{\omega}^{1,p}(G)\) admits a bounded approximate identity if and only if G is discrete. In addition, we prove that amenability of this algebra implies that G is discrete and amenable. Moreover, we discuss the converse of this result.  相似文献   

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