We present a new class of reflexive l(p) saturated Banach spaces x(p) for 1 < p < infinity with rather tight structure. The norms of these spaces are defined with the use of a modification of the standard method yielding hereditarily indecomposable Banach spaces. The space x(p) does not embed into a space with an unconditional basis and for any analytic decomposition into two subspaces, it is proved that one of them embeds isomorphically into the l(p)-sum of a sequence of finite dimensional normed spaces. We also study the space of operators of X-p.
Carando, Daniel
Dimant, Veronica
Sevilla-Peris, Pablo
Villafane, Roman
We study extendibility of diagonal multilinear operators from l(p) to l(p) spaces. We determine the values of and for which every diagonal -linear operator is extendible, and those for which the only extendible ones are integral. We address the same question for multilinear forms on l(p).
In this paper we establish global L-p(R-n)-regularity properties of Fourier integral operators. The orders of decay of the amplitude are determined for operators to be bounded on L-p(R-n), 1 < p < infinity, as well as to be bounded from Hardy space H-1(R-n) to L-1(R-n). This extends local L-p-regularity properties of Fourier integral operators, as well as results of global L-2(R-n) boundedness, to the global setting of L-p(R-n). Global boundedness in weighted Sobolev spaces W-s(sigma,p) (R-n) is also established, and applications to hyperbolic partial differential equations are given.
We estimate the observable diameter of the l (p) -product space X (n) of an mm-space X by using the limit formula in our previous paper (Ozawa and Shioya, Math. Zeit. (to appear)). The idea of our proof is based on Gromov's book (In: Metric structures for Riemannian and non-Riemannian spaces, 2007). As a corollary we obtain the phase transition property of under a uniform discreteness condition.
Let (M (n) , g)(n =3D 3) be an n-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by R and R mI the scalar curvature and the trace-free Riemannian curvature tensor of M, respectively. The main result of this paper states that R mI goes to zero uniformly at infinity if for , the L (p) -norm of R mI is finite. Moreover, If R is positive, then (M (n) , g) is compact. As applications, we prove that (M (n) , g) is isometric to a spherical space form if for , R is positive and the L (p) -norm of R mI is pinched in [0, C (1)), where C (1) is an explicit positive constant depending only on n, p, R and the Yamabe constant. We give an isolation theorem of the trace-free Ricci curvature tensor of compact locally conformally flat Riemannian n-manifolds with constant positive scalar curvature, which extends Theorem 1 of Hebey and M. Vaugon (J. Geom. Anal. 6, 531-553, 1996). This result is sharp, and we can precisely characterize the case of equality. In particular, when n =3D 4, we recover results by Gursky (Indiana Univ. Math. J. 43, 747-774, 1994; Ann. Math. 148, 315-337, 1998).
Charpentier, Clement
Montassier, Mickael
Raspaud, Andre
Let p and q be positive integers. An L(p,q)-labeling of a graph G with a span s is a labeling of its vertices by integers between 0 and s such that adjacent vertices of G are labeled using colors at least p apart, and vertices having a common neighbor are labeled using colors at least q apart. We denote by lambda(p,q) (G) the least integer k such that G has an L(p,q)-labeling with span k. The maximum average degree of a graph G, denoted by , is the maximum among the average degrees of its subgraphs (i.e. MAd (G)=max{2 vertical bar E(H)vertical bar/vertical bar V(H)vertical bar; H subset of G}). We consider graphs G with Mad(G)<10/3, 3 and 14/5. These sets of graphs contain planar graphs with girth 5, 6 and 7 respectively. We prove in this paper that every graph G with maximum average degree m and maximum degree Delta has: -lambda(p,q)(G)<=(2q-1)Delta+6p+10q-8 if m<10/3 and p >= 2q. -lambda(p,q)(G)<=(2q-1)Delta+4p+14q-9 if m<10/3 and 2q>p. -lambda(p,q)(G)<=(2q-1)Delta+4p+6q-5 if m<3. -lambda(p,q)(G)<=(2q-1)Delta+4p+4q-4 if m<14/5. We give also some refined bounds for specific values of p, q, or Delta. By the way we improve results of Lih and Wang (SIAM J. Discrete Math. 17(2):264-275, 2003).
Let K be a commutative hypergroup. At first, we characterize the space of multipliers on L-p(K, m). Then, we investigate the multipliers on L-1(S, pi) and L-2(S, pi), where S is the dual space of K, i.e., S = supp pi, pi is the Plancherel measure of K.
The inverse document frequency (IDF) is prevalently utilized in the bag-of-words-based image retrieval application. The basic idea is to assign less weight to terms with high frequency, and vice versa. However, in the conventional IDF routine, the estimation of visual word frequency is coarse and heuristic. Therefore, its effectiveness is largely compromised and far from optimal. To address this problem, this paper introduces a novel IDF family by the use of Lp-norm pooling technique. Carefully designed, the proposed IDF considers the term frequency, document frequency, the complexity of images, as well as the codebook information. We further propose a parameter tuning strategy, which helps to produce optimal balancing between TF and pIDF weights, yielding the so-called Lp-norm IDF (pIDF). We show that the conventional IDF is a special case of our generalized version, and two novel IDFs, i.e., the average IDF and the max IDF, can be defined from the concept of pIDF. Further, by counting for the term-frequency in each image, the proposed pIDF helps to alleviate the visual word burstiness phenomenon. Our method is evaluated through extensive experiments on four benchmark data sets (Oxford 5K, Paris 6K, Holidays, and Ukbench). We show that the pIDF works well on large scale databases and when the codebook is trained on irrelevant data. We report an mean average precision improvement of as large as +13.0% over the baseline TF-IDF approach on a 1M data set. In addition, the pIDF has a wide application scope varying from buildings to general objects and scenes. When combined with postprocessing steps, we achieve competitive results compared with the state-of-the-art methods. In addition, since the pIDF is computed offline, no extra computation or memory cost is introduced to the system at all. =20
In the first part of the paper we study the minimal and maximal extension of a class of weighted pseudodifferential operators in the Frechet space L loc p(Omega). In the second one non homogeneous microlocal properties are introduced and propagation of Sobolev singularities for solutions to (pseudo)differential equations is given. For both the arguments actual examples are provided.
We show that for any 1 <=3D p <=3D infinity, the family of random vectors uniformly distributed on hyperplane projections of the unit ball of l(p)(n) verify the variance conjecture Var vertical bar X vertical bar(2) <=3D C max(xi is an element of Sn-1) E < X, xi >(2) E vertical bar X vertical bar(2), where C depends on p but not on the dimension n or the hyperplane. We will also show a general result relating the variance conjecture for a random vector uniformly distributed on an isotropic convex body and the variance conjecture for a random vector uniformly distributed on any Steiner symmetrization of it. As a consequence we will have that the class of random vectors uniformly distributed on any Steiner symmetrization of an l(p)(n) - ball verify the variance conjecture.