共查询到20条相似文献,搜索用时 46 毫秒
1.
The rangeI α (L p ) of the Riesz potential operator, defined in the sense of distributions in the casep≥n/α, is shown to consist of regular distributions. Moreover, it is shown thatI α (L p ) ?L p loc (R n ) for all 1≤p<∞ and 0<α<∞. The distribution space used is that of Lizorkin, which is invariant with respect to the Riesz operator. 相似文献
2.
Y. Q. Yan 《Functional Analysis and Its Applications》2005,39(4):321-323
Let φ be an N-function. Then the normal structure coefficients N and the weakly convergent sequence coefficients WCS of the Orlicz function spaces L φ[0, 1] generated by φ and equipped with the Luxemburg and Orlicz norms have the following exact values. (i) If F φ(t) = t ?(t)/φ(t) is decreasing and 1 < C φ < 2 (where \(C_\Phi = \lim _{t \to + \infty } t\varphi (t)/\Phi (t)\)), then N(L (φ)[0, 1]) = N(L φ[0, 1]) = WCS(L (φ)[0, 1]) = WCS(L φ[0, 1]) = 21?1/Cφ. (ii) If F φ(t) is increasing and C φ > 2, then N(L (φ)[0, 1]) = N(L φ[0, 1]) = WCS(L (φ)[0, 1]) = WCS(L φ[0, 1]) = 21/Cφ. 相似文献
3.
K. Kazarian V. N. Temlyakov 《Proceedings of the Steklov Institute of Mathematics》2013,280(1):181-190
We consider a weighted L p space L p (w) with a weight function w. It is known that the Haar system H p normalized in L p is a greedy basis of L p , 1 < p < ∞. We study a question of when the Haar system H p w normalized in L p (w) is a greedy basis of L p (w), 1 < p < ∞. We prove that if w is such that H p w is a Schauder basis of L p (w), then H p w is also a greedy basis of L p (w), 1 < p < ∞. Moreover, we prove that a subsystem of the Haar system obtained by discarding finitely many elements from it is a Schauder basis in a weighted norm space L p (w); then it is a greedy basis. 相似文献
4.
《Journal of Mathematical Analysis and Applications》1987,127(1):237-245
This paper is motivated by [2], where we have given necessary and sufficient conditions for a given basis P in the space of polynomials to be orthogonal with respect to the measure ϱdφ for a certain function ϱ ϵ L2(dφ). Let P = {pi: i = 0, 1, …}, p0 = 1. Then the conditions are (1) a multivariate analog of the three-term recurrence relation holds, see Section 4 for details; and (2) {qi = ∑j = 0∞ cij Pj, i = 0, 1, …} is a φ-orthonormal basis in the space of polynomials for some coefficients cij such that ∑i = 0∞ ci02 <-∞. This paper provides an algebraic condition (a condition on the coefficients ci0) such that ϱ satisfies ∥p∥ <B, Bϵ (0, ∞], and has a cone-positivity property. In particular, our results imply that ϱ is nonnegative a.e. if ∑i = 0∞ ci02 < ∞ and ∑jϵ Sk cj0 qj defines nonnegative polynomials for certain finite sets S1, S2, … of integers. 相似文献
5.
A non-zero vector-valued sequence u ∈ ?q(X′) is a cover for a subset M of ?P(X) if, for some 0 < α ≤ 1, ∥u * h∥ ∞ ≥ α ∥u∥q ∥h∥p for all h ∈ M. Covers of ?1 = ?1(R) are important in worst case system identification in ?1 and in the reconstruction of elements in a normed space from corrupted functional values. We investigate the existence of covers for certain naturally occurring subspaces of ?p(X). We show that there exist finitely supported covers for some subspaces, and obtain lower bounds for their ’lengths’. We also obtain similar results for covers associated with convolution products for spaces of measurable vector-valued functions defined on the positive real axis. 相似文献
6.
Let θ ∈ (0, 1), λ ∈ [0, 1) and p, p 0, p 1 ∈ (1,∞] be such that (1 ? θ)/p 0 + θ/p 1 = 1/p, and let φ, φ0, φ1 be some admissible functions such that φ, φ0 p/p0 and φ1 p/p1 are equivalent. We first prove that, via the ± interpolation method, the interpolation L φ0 p0),λ (X), L φ1 p1), λ (X), θ> of two generalized grand Morrey spaces on a quasi-metric measure space X is the generalized grand Morrey space L φ p),λ (X). Then, by using block functions, we also find a predual space of the generalized grand Morrey space. These results are new even for generalized grand Lebesgue spaces. 相似文献
7.
M. G. Grigoryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(4):205-218
Let χ = {χ n } n=0 ∞ be the Haar system normalized in L 2(0, 1) and M = {M s } s=1 ∞ be an arbitrary, increasing sequence of nonnegative integers. For any subsystem of χ of the form {φ k } = χS = {χ n } n∈S , where S = S(M) = {n k } k=1 ∞ = {n ∈ V[p]: p ∈ M}, V[0] = {1, 2} and V[p] = {2 p + 1, 2 p + 2, …, 2 p+1} for p = 1, 2, … a series of the form Σ i=1 ∞ a i φ i with a i ↘ 0 is constructed, that is universal with respect to partial series in all classes L r (0, 1), r ∈ (0, 1), in the sense of a.e. convergence and in the metric ofL r (0, 1). The constructed series is universal in the class of all measurable, finite functions on [0, 1] in the sense of a.e. convergence. It is proved that there exists a series by Haar system with decreasing coefficients, which has the following property: for any ? > 0 there exists a measurable function µ(x), x ∈ [0, 1], such that 0 ≤ µ(x) ≤ 1 and |{x ∈ [0, 1], µ(x) ≠ = 1}| < ?, and the series is universal in the weighted space L µ[0, 1] with respect to subseries, in the sense of convergence in the norm of L µ[0, 1]. 相似文献
8.
Djordjije Vujadinović 《Integral Equations and Operator Theory》2013,76(2):213-224
In this paper we obtain an estimate of the norm of the Bergman projection from L p (D, dλ) onto the Besov space B p , 1 < p < + ∞. The result is asymptotically sharp when p → + ∞. Further for the case P : L 1(D, dλ) → B 1, we consider some weak type inequalities with the corresponding spaces. 相似文献
9.
Let Δ(x) = max {1 - ¦x¦, 0} for all x ∈ ?, and let ξ[0,1) be the characteristic function of the interval 0 ≤x < 1. Two seminal theorems of M. Jodeit assert that A and ξ[0,1) act as summability kernels convertingp-multipliers for Fourier series to multipliers forL P (?). The summability process corresponding to Δ extendsL P (T)-multipliers from ? to ? by linearity over the intervals [n, n + 1],n ∈ ?, when 1 ≤p < ∞, while the summability process corresponding to ξ[0,1) extends LP(T)-multipliers by constancy on the intervals [n, n + 1),n ∈ ?, when 1 <p < ∞. We describe how both these results have the following complete generalization: for 1 ≤p < ∞, an arbitrary compactly supported multiplier forL P (?) will act as a summability kernel forL P (T)-multipliers, transferring maximal estimates from LP(T) to LP(?). In particular, specialization of this maximal theorem to Jodeit’s summability kernel ξ[0, 1) provides a quick structural way to recover the fact that the maximal partial sum operator on LP(?), 1 <p < ∞, inherits strong type (p,p)-boundedness from the Carleson-Hunt Theorem for Fourier series. Another result of Jodeit treats summability kernels lacking compact support, and we show that this aspect of multiplier theory sets up a lively interplay with entire functions of exponential type and sampling methods for band limited distributions. 相似文献
10.
E. D. Nursultanov 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):185-202
Let (X, Y) be a pair of normed spaces such that X ? Y ? L 1[0, 1] n and {e k } k be an expanding sequence of finite sets in ? n with respect to a scalar or vector parameter k, k ∈ ? or k ∈ ? n . The properties of the sequence of norms $\{ \left\| {S_{e_k } (f)} \right\|x\} _k $ of the Fourier sums of a fixed function f ∈ Y are studied. As the spaces X and Y, the Lebesgue spaces L p [0, 1], the Lorentz spaces L p,q [0, 1], L p,q [0, 1] n , and the anisotropic Lorentz spaces L p,q*[0, 1] n are considered. In the one-dimensional case, the sequence {e k } k consists of segments, and in the multidimensional case, it is a sequence of hyperbolic crosses or parallelepipeds in ? n . For trigonometric polynomials with the spectrum given by step hyperbolic crosses and parallelepipeds, various types of inequalities for different metrics in the Lorentz spaces L p,q [0, 1] n and L p,q*[0, 1] n are obtained. 相似文献
11.
Hong-Quan Li 《Comptes Rendus Mathematique》2004,338(1):31-34
In this Note, we study the behavior of the Hardy–Littlewood maximal function M on cusp manifolds in terms of the growth of the volume of the base space. In particular, we prove that for all 1<p0<+∞ fixed, there exists such a manifold on which M is bounded on Lp for p>p0 but not for 1?p<p0. To cite this article: H.-Q. Li, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
12.
We prove that if E is a rearrangement-invariant space, then a boundedly complete basis exists in E, if and only if one of the following conditions holds: 1) E is maximal and E ≠ L 1[0, 1]; 2) a certain (any) orthonormal system of functions from L ∞[0, 1], possessing the properties of the Schauder basis for the space of continuous on [0, 1] functions with the norm L ∞, represents a boundedly complete basis in E. As a corollary, we state the following assertion: Any (certain) orthonormal system of functions from L ∞[0, 1], possessing the properties of the Schauder basis for the space of continuous on [0, 1] functions with the norm L ∞, represents a spanning basis in a separable rearrangement-invariant space E, if and only if the adjoint space E* is separable. We prove that in any separable rearrangement-invariant space E the Haar system either forms an unconditional basis, or a strongly conditional one. The Haar system represents a strongly conditional basis in a separable rearrangement-invariant space, if and only if at least one of the Boyd indices of this space is trivial. 相似文献
13.
S. V. Astashkin 《Functional Analysis and Its Applications》2013,47(2):148-151
We show that, for a broad class of symmetric spaces on [0, 1], the complementability of the subspace generated by independent functions f k (k = 1, 2,…) is equivalent to the complementability of the subspace generated by the disjoint translates $\bar f_k (t) = f_k (t - k + 1)\chi _{[k - 1,k]} (t)$ of these functions in some symmetric space Z X 2 on the semiaxis [0,∞). Moreover, if Σ k=1 ∞ m(supp f k ) ? 1, then Z X 2 can be replaced by X itself. This result is new even in the case of L p -spaces. A series of consequences is obtained; in particular, for the class of symmetric spaces, a result similar to a well-known theorem of Dor and Starbird on the complementability in L p [0, 1] (1 ? p < ∞) of the subspace [f k ] generated by independent functions provided that it is isomorphic to the space l p is obtained. 相似文献
14.
Pekka J. Nieminen Eero Saksman 《Journal of Mathematical Analysis and Applications》2004,298(2):501-522
Let φ and ψ be analytic self-maps of the unit disc, and denote by Cφ and Cψ the induced composition operators. The compactness and weak compactness of the difference T=Cφ−Cψ are studied on Hp spaces of the unit disc and Lp spaces of the unit circle. It is shown that the compactness of T on Hp is independent of p∈[1,∞). The compactness of T on L1 and M (the space of complex measures) is characterized, and examples of φ and ψ are constructed such that T is compact on H1 but non-compact on L1. Other given results deal with L∞, weakly compact counterparts of the previous results, and a conjecture of J.E. Shapiro. 相似文献
15.
We deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L ∞ coefficients whose prototypes are the p-Laplacian (2N/(N + 1) < p < 2) and the porous medium equation (((N ? 2)/N)+ < m < 1). We prove existence of and sharp pointwise estimates from above and from below for the fundamental solutions. Our results can be extended to general non-negative L 1 initial data. 相似文献
16.
Qingying Bu 《Journal of Functional Analysis》2003,204(1):101-121
Let X be a (real or complex) Banach space and 1<p,p′<∞ such that 1/p+1/p′=1. Then , the injective tensor product of Lp[0,1] and X, has the Radon-Nikodym property (resp. the analytic Radon-Nikodym property, the near Radon-Nikodym property, contains no copy of c0, is weakly sequentially complete) if and only if X has the same property and each continuous linear operator from Lp′[0,1] to X is compact. 相似文献
17.
Jianyong WANG 《数学年刊B辑(英文版)》2013,34(4):541-556
The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p). 相似文献
18.
We study here a biharmonic equation in an exterior domain of . We give in Lp theory, with 1<p<∞ existence, uniqueness and regularity results. To cite this article: C. Amrouche, M. Fontes, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
19.
G. C. Kyriazis 《Constructive Approximation》1995,11(2):141-164
We give sufficient conditions on a single function ? so that the principal shift-invariant space generated by ? provides a prescribed order of approximation inL p (R d ), 1<p<∞, and inH p (R d ), 0<p≤1. In particular, our conditions are given in terms of $\hat \varphi$ and are satisfied even when ? does not decay quickly at infinity. 相似文献
20.