共查询到20条相似文献,搜索用时 0 毫秒
1.
Let (M n , g)(n ≥ 3) be an n-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by R and R m? the scalar curvature and the trace-free Riemannian curvature tensor of M, respectively. The main result of this paper states that R m? goes to zero uniformly at infinity if for \(p\geq \frac n2\), the L p -norm of R m? 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 \(p\geq \frac n2\), R is positive and the L p -norm of R m? 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 = 4, we recover results by Gursky (Indiana Univ. Math. J. 43, 747–774, 1994; Ann. Math. 148, 315–337, 1998). 相似文献
2.
Using measure-capacity inequalities we study new functional inequalities, namely L
q
-Poincaré inequalities
and L
q
-logarithmic Sobolev inequalities
for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media
equation
for m ≥ 1, in terms of L
2-norms and entropies.
相似文献
3.
L. Olsen 《Monatshefte für Mathematik》2005,146(2):143-157
For a probability measure μ on a subset of
, the lower and upper Lq-dimensions of order
are defined by
We study the typical behaviour (in the sense of Baire’s category) of the Lq-dimensions
and
. We prove that a typical measure μ is as irregular as possible: for all q ≥ 1, the lower Lq-dimension
attains the smallest possible value and the upper Lq-dimension
attains the largest possible value. 相似文献
4.
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
5.
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
6.
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
7.
8.
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
9.
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
10.
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
11.
Milutin Dostanić 《Journal d'Analyse Mathématique》2008,104(1):13-23
It is shown that the Berezin transform B on L
p
(D), where D is the unit disc, has norm
. Furthermore, the norms of a family of operators (on L
p
(D)) whose kernels are moduli of Bergman type kernels are also calculated.
Partially supported by MNZZS, Grant
ON144010 相似文献
12.
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
13.
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 H⊂M 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
14.
A. I. Kamzolov 《Moscow University Mathematics Bulletin》2007,62(4):158-162
Asymptotic estimates of L q -norms of partial sums of Fourier-Legendre series of functions from L p [?1; 1] are obtained. 相似文献
15.
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
16.
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
17.
F. Abtahi 《Acta Mathematica Hungarica》2011,133(4):324-331
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
18.
In this paper, we establish the preserving log-convexity of linear transformation associated with p, q-analogue of Pascal triangle, i.e., if the sequence of nonnegative numbers {xn}n is logconvex, then \({y_n} = {\sum\nolimits_{k = 0}^n {\left[ {\frac{n}{k}} \right]} _{pq}}{x_k}\) so is it for q ≠ p ≥ 1. 相似文献
19.
20.
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