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1.
The purpose of this paper is to use semiclassical analysis to unify and generalize L
p estimates on high energy eigenfunctions and spectral clusters. In our approach these estimates do not depend on ellipticity
and order, and apply to operators which are selfadjoint only at the principal level. They are estimates on weakly approximate
solutions to semiclassical pseudodifferential equations.
Submitted: May 11, 2006. Accepted: September 19, 2006. 相似文献
2.
A. L. Kuz’mina 《Russian Mathematics (Iz VUZ)》2008,52(7):8-14
We study Besicovitch-type spaces of generalized almost periodic functions. The main result is a theorem on representation of linear continuous functionals that is similar to the classical result of F. Riesz. 相似文献
3.
T. S. Kopaliani 《Ukrainian Mathematical Journal》2008,60(12):2006-2014
We point out that if the Hardy–Littlewood maximal operator is bounded on the space L
p(t)(ℝ), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ, then the well-known characterization of the spaces L
p
(ℝ), 1 < p < ∞, by the Littlewood–Paley theory extends to the space L
p(t)(ℝ). We show that, for n > 1 , the Littlewood–Paley operator is bounded on L
p(t) (ℝ
n
), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ
n
, if and only if p(t) = const.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1709–1715, December, 2008. 相似文献
4.
If (N,t) ({\cal N},\tau) is a finite von Neumann algebra and if (M,n) ({\cal M},\nu) is an infinite von Neumann algebra, then Lp(M,n) L_{p}({\cal M},\nu) does not Banach embed in Lp(N,t) L_{p}({\cal N},\tau) for all p ? (0,1) p\in (0,1) . We also characterize subspaces of $ L_{p}({\cal N},\tau),\ 0< p <1 $ L_{p}({\cal N},\tau),\ 0< p <1 containing a copy of lp. 相似文献
5.
We use microlocal and paradifferential techniques to obtain L
8 norm bounds for spectral clusters associated with elliptic second-order operators on two-dimensional manifolds with boundary.
The result leads to optimal L
q
bounds, in the range 2⩽q⩽∞, for L
2 - normalized spectral clusters on bounded domains in the plane and, more generally, for two-dimensional compact manifolds
with boundary. We also establish new sharp L
q
estimates in higher dimensions for a range of exponents q̅n⩽q⩽∞.
The authors were supported by the National Science Foundation, Grants DMS-0140499, DMS-0099642, and DMS-0354668. 相似文献
6.
The Hilbert and Riesz transforms can be characterized up to scalar as the translation invariant operators that satisfy additionally
certain relative invariance of conformal transformation groups. In this article, we initiate a systematic study of translation
invariant operators from group theoretic viewpoints, and formalize a geometric condition that characterizes specific multiplier
operators uniquely up to scalar by means of relative invariance of affine subgroups. After providing some interesting examples
of multiplier operators having “large symmetry”, we classify which of these examples can be extended to continuous operators
on L
p
(R
n
) (1 < p < ∞).
T. Kobayashi was partially supported by Grant-in-Aid for Scientific Research 18340037, Japan Society for the Promotion of
Science. A. Nilsson was partially supported by Japan Society for the Promotion of Science. 相似文献
7.
Satish Shirali 《Ricerche di matematica》2008,57(1):43-54
For a subadditive fuzzy measure (not assumed finite), a Minkowski type triangle inequality, with Choquet integrals in place
of Lebesgue integrals, is shown to hold. It is immediate that the set of functions for which a certain positive power of the
absolute values have finite Choquet integrals is closed under addition, leading to a linear space analogous to the Lebesgue
space L
p
, with a metric related to the integral of that power. Under the additional condition that the subadditive fuzzy measure is
inner continuous (Sugeno), the space is shown to be complete. Consequences of the Minkowski type inequality are illustrated
in two specific instances.
相似文献
8.
Jia Gao 《高校应用数学学报(英文版)》2007,22(2):174-180
Let L^p(Ω, H^n) indicate the L^P-space of the maps for Heisenberg group target. In this paper some new properties are obtained for the space L^p(Ω, H^n) 相似文献
9.
In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace τ, and {α
t
}, a strongly continuous extension to L
p
(M, τ) of a semigroup of absolute contractions on L
1(M, τ). By means of a non-commutative Banach Principle we prove for a Besicovitch function b and x ∊ L
p
(M, τ), that the averages 1/T ∫0
T
b(t)α
t
(x)dt converge bilateral almost uniformly in L
p
(M, τ) as T → 0.
Communicated by Dénes Petz 相似文献
10.
Michael J. Puls 《Archiv der Mathematik》2007,88(6):500-506
Let p be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first L
p
-cohomology space of some groups that have one end. We also make a connection between the first L
p
-cohomolgy space and the Floyd boundary of the Cayley graph of a group. We apply the result about Floyd boundaries to show
that there exists a real number p such that the first L
p
-cohomology space of a nonelementary hyperbolic group does not vanish.
Received: 4 August 2006 Revised: 2 November 2006 相似文献
11.
Li Wenming 《分析论及其应用》2002,18(3):86-92
Using the maximal function characterization of Hardy spaces, we study the interpolation spaces be-tween H1 and L∞ on spaces of homogeneous type. 相似文献
12.
Let Γ be a C∞ curve in Rn and μ be the measure induced by Lebesgue measure on Γ,multiplied by a smooth cut-off function.In this paper,we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ. 相似文献
13.
We will discuss about the mapping property of Radon transform on L
p
spaces with power weight. It will be shown that the Pitt’s inequality together with the weighted version of Hardy-Littlewood-Sobolev
lemma imply weighted inequality for the Radon transform. 相似文献
14.
15.
In [1], we defined c(G), q(G) and p(G). In this paper we will show that if G is a p-group, where p is an odd prime and |G| ≤ p
4, then c(G) = q(G) = p(G). However, the question of whether or not there is a p-group G with strict inequality c(G) = q(G) < p(G) is still open. 相似文献
16.
ChangJian Zhao 《中国科学A辑(英文版)》2008,51(12):2172-2188
In this paper the author first introduce a new concept of L
p
-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L
p
intersection body to L
p
-mixed intersection body. Inequalities for L
p
-dual mixed volumes of L
p
-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.
This work was supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065) and the Foundation
of the Education Department of Zhejiang Province of China (Grant No. 20050392) 相似文献
17.
Wu Yang YU Dong Hua WU Gang Song LENG 《数学学报(英文版)》2007,23(11):1937-1948
The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established. 相似文献
18.
Eiichi Nakai 《数学学报(英文版)》2008,24(8):1243-1268
Let X = (X, d,μ) The purpose of this paper is to be a space of homogeneous type in the sense of Coifman and Weiss. generalize the definition of Hardy space H^P(X) and prove that the generalized Hardy spaces have the same property as H^P(X). Our definition includes a kind of Hardy- Orlicz spaces and a kind of Hardy spaces with variable exponent. The results are new even for the R^n case. Let (X, δ, μ) be the normalized space of (X, d, μ) in the sense of Macias and Segovia. We also study the relations of our function spaces for (X, d, μ) and (X, δ,μ). 相似文献
19.
Pierre Pansu 《Potential Analysis》2007,27(2):151-165
The L
p
-cohomology in degree 1 of Riemannian homogeneous spaces is computed. It turns out that reduced cohomology does not vanish
exactly for spaces quasiisometric to negatively curved homogeneous spaces.
相似文献
20.
G. Barbatis 《Mathematische Zeitschrift》2007,255(4):877-896
We obtain a series improvement to higher-order L
p
-Rellich inequalities on a Riemannian manifold M. The improvement is shown to be sharp as each new term of the series is added.
相似文献