共查询到20条相似文献,搜索用时 15 毫秒
1.
Yaroslav Kopylov 《Archiv der Mathematik》2007,89(1):87-96
We consider some problems concerning the L
p,q
-cohomology of Riemannian manifolds. In the first part, we study the question of the normal solvability of the operator of
exterior derivation on a surface of revolution M considered as an unbounded linear operator acting from Lpk (M) into Lk+1q (M). In the second part, we prove that the first L
p,q-cohomology of the general Heisenberg group is nontrivial, provided that p < q.
Received: 17 January 2006
Supported by INTAS (Grant 03–51–3251) and the State Maintenance Program for the Leading Scientific Schools of the Russian
Federation (Grants NSh 311.2003.1, NSh 8526.2006.1). 相似文献
2.
<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-Betti numbers of one-relator groups
We determine the L
2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the
L
2-cohomology of left-orderable groups, and deduce the non-L
2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free.
Warren Dicks was Funded by the DGI (Spain) through Project BFM2003-06613. 相似文献
3.
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
4.
Sun-Sig Byun 《Journal of Evolution Equations》2007,7(3):415-428
This work treats Lp regularity theory for weak solutions of parabolic equations in divergence form with discontinuous coefficients on nonsmooth
domains. We essentially obtain an optimal condition on the coefficients under which the global W1,p regularity theory holds.
This work was supported by SNU foundation in 2005. 相似文献
5.
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
6.
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
7.
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
8.
9.
R. A. Lasuriya 《Ukrainian Mathematical Journal》2005,57(4):600-609
We establish estimates for the rate of convergence of a group of deviations on a sphere in the space L(S
m
), m ≥ 3.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 496–504, April, 2005. 相似文献
10.
Lawrence C. Evans Ovidiu Savin 《Calculus of Variations and Partial Differential Equations》2008,32(3):325-347
We propose a new method for showing C
1, α
regularity for solutions of the infinity Laplacian equation and provide full details of the proof in two dimensions. The
proof for dimensions n ≥ 3 depends upon some conjectured local gradient estimates for solutions of certain transformed PDE.
LCE is supported in part by NSF Grant DMS-0500452. OS was supported in part by the Miller Institute for Basic Research in
Science, Berkeley. 相似文献
11.
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
12.
Xiang-Dong Li 《Journal of Geometric Analysis》2010,20(2):354-387
We prove some Sobolev inequalities on differential forms over a class of complete non-compact Riemannian manifolds with suitable
geometric conditions. Moreover, we establish some L
p,q
-estimates and existence theorems of the Cartan-De Rham equation and the Hodge systems. As applications, we prove some vanishing
theorems of the L
p,q
-cohomology and prove the L
q
-solvability of the nonlinear p-Laplace equation on forms on complete non-compact Riemannian manifolds with suitable geometric conditions. 相似文献
13.
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
14.
We investigate R-bounded representations
, where X is a Banach space and G is a lca group. Observing that Ψ induces a (strongly continuous) group homomorphism
, we are then able to analyze certain classical homomorphisms U (e.g. translations in Lp (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators.
Dedicated to the memory of H. H. Schaefer 相似文献
15.
We study extension of operators T: E→ L0([0, 1]), where E is an F–function space and L0([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the properties of such domains. The main tool is the integration of scalar functions with respect to stochastic
measures and the corresponding spaces of integrable functions.
Partially supported by D.G.I. #MTM2006-13000-C03-01 (Spain). 相似文献
16.
Milutin R. Dostanić 《Czechoslovak Mathematical Journal》2008,58(2):569-575
We give some explicit values of the constants C
1 and C
2 in the inequality C
1/sin(π/p) ⩽ |P|
p
⩽ C
2/sin(π/p) where |P|
p
denotes the norm of the Bergman projection on the L
p
space.
Partially supported by MNZZS Grant No. ON144010. 相似文献
17.
We study the Cauchy problem for time-dependent diffusion operators with singular coefficients on L1-spaces induced by infinitesimal invariant measures. We give sufficient conditions on the coefficients such that the Cauchy-Problem is well-posed. We construct associated diffusion processes with the help of the theory of generalized Dirichlet forms. We apply our results in particular to construct a large class of Nelson-diffusions that could not been constructed before. 相似文献
18.
We study Lp-viscosity solutions of fully nonlinear, second-order, uniformly elliptic partial differential equations (PDE) with measurable terms and quadratic nonlinearity. We present a sufficient condition under which the maximum principle holds for Lp-viscosity solution. We also prove stability and existence results for the equations under consideration. 相似文献
19.
Igor V. Dolgachev 《Proceedings of the Steklov Institute of Mathematics》2009,264(1):48-55
We show that the plane Cremona group over a field of characteristic p > 0 does not contain elements of order of power of p larger than 2. We also describe conjugacy classes of elements of order p
2.
To the memory of Vasily Iskovskikh 相似文献
20.
Matthias Geissert 《Numerische Mathematik》2007,108(1):121-149
In this paper, we present applications of discrete maximal L
p
regularity for finite element operators. More precisely, we show error estimates of order h
2 for linear and certain semilinear problems in various L
p
(Ω)-norms. Discrete maximal regularity allows us to prove error estimates in a very easy and efficient way. Moreover, we also
develop interpolation theory for (fractional powers of) finite element operators and extend the results on discrete maximal
L
p
regularity formerly proved by the author.
The author was supported by the DFG-Graduiertenkolleg 853. 相似文献