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1.
Alessandro Veneruso 《Monatshefte für Mathematik》2000,130(3):231-252
Let be the Heisenberg group of dimension . Let be the partial sub-Laplacians on and T the central element of the Lie algebra of . For any we prove that the operator is bounded on the Hardy spaces , if the function m satisfies a Hrmander-type condition on which depends on . We also obtain analogous results for the operators and , where the function m satisfies analogous H?rmander-type conditions on and on , respectively. Here is the Kohn-Laplacian on .
(Received 28 July 1999; in final form 6 March 2000) 相似文献
2.
3.
In this paper we consider oscillatory integral operators with strong singularities on . We obtain sharp decay estimates for L2 operator norm. We also obtain Hp estimates for difference of oscillatory strongly singular integral operators and strongly singular integral operators, which gives Lp mapping properties of oscillatory strongly singular integral operators. 相似文献
4.
Let M be a general complete Riemannian manifold and consider a Schr?dinger operator −Δ+V on L
2(M). We prove Cwikel–Lieb–Rozenblum as well as Lieb–Thirring type estimates for −Δ+V. These estimates are given in terms of the potential and the heat kernel of the Laplacian on the manifold. Some of our results
hold also for Schr?dinger operators with complex-valued potentials. 相似文献
5.
Both oscillatory integral operators and level set operators appear naturally in the study of properties of degenerate Fourier
integral operators (such as generalized Randon transforms). The properties of oscillatory integral operators have a longer
history and are better understood. On the other hand, level set operators, while sharing many common characteristics with
oscillatory integral operators, are easier to handle.
We study L2-estimates on level set operators in dimension two and compare them with what is known about oscillatory integral operators.
The cases include operators with non-degenerate phase functions and the level set version of Melrose-Taylor transform (as
an example of a degenerate phase function). The estimates are formulated in terms of the Newton polyhedra and type conditions. 相似文献
6.
We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders
of derivatives belong to certain types of modulation space. We prove continuity and Schatten–von Neumann properties of such
operators when acting on L
2. 相似文献
7.
We establish sharp L
2-Sobolev estimates for classes of pseudodifferential operators with singular symbols [Guillemin and Uhlmann (Duke Math J 48:251–267,
1981), Melrose and Uhlmann (Commun Pure Appl Math 32:483–519, 1979)] whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered
include both singular integral operators along curves in
\mathbb R2{\mathbb R^2} with simple inflection points and normal operators arising in linearized seismic imaging in the presence of fold caustics
[Felea (Comm PDE 30:1717–1740, 2005), Felea and Greenleaf (Comm PDE 33:45–77, 2008), Nolan (SIAM J Appl Math 61:659–672, 2000)]. 相似文献
8.
In this paper, the authors consider a class of maximal multilinear singular integral operators
and maximal multilinear oscillatory singular integral operators with standard Calderón–Zygmund
kernels, and obtain their boundedness on L
p
(ℝ
n
) for 1 < p < ∞.
Research supported by Professor Xu Yuesheng’s Research Grant in the program of "One hundred Distinguished
Young Scientists" of the Chinese Academy of Sciences 相似文献
9.
L
2 estimates are obtained for some oscillatory singular integral operators with analytic phrases by using the technology of
almost orthogonality, oscillatory estimates and size estimates. 相似文献
10.
This paper systematically studies numerical solution of fourth order problems in any dimensions by use of the Morley–Wang–Xu
(MWX) element discretization combined with two-grid methods (Xu and Zhou (Math Comp 69:881–909, 1999)). Since the coarse and fine finite element spaces are nonnested, two intergrid transfer operators are first constructed
in any dimensions technically, based on which two classes of local and parallel algorithms are then devised for solving such
problems. Following some ideas in (Xu and Zhou (Math Comp 69:881–909, 1999)), the intrinsic derivation of error analysis for nonconforming finite element methods of fourth order problems (Huang et al.
(Appl Numer Math 37:519–533, 2001); Huang et al. (Sci China Ser A 49:109–120, 2006)), and the error estimates for the intergrid transfer operators, we prove that the discrete energy errors of the two classes
of methods are of the sizes O(h + H
2) and O(h + H
2(H/h)(d−1)/2), respectively. Here, H and h denote respectively the mesh sizes of the coarse and fine finite element triangulations, and d indicates the space dimension of the solution region. Numerical results are performed to support the theory obtained and
to compare the numerical performance of several local and parallel algorithms using different intergrid transfer operators. 相似文献
11.
Christine Laurent-Thiébaut Jürgen Leiterer 《Annali di Matematica Pura ed Applicata》2001,180(1):59-70
Using Serre duality in CR manifolds and integral operators for the solution of the tangential Cauchy–Riemann equation with compact support, we prove
a separation theorem of Andreotti–Vesentini type for the -cohomology in q-concave real hypersurfaces.
Received: February 17, 1999?Published online: May 10, 2001 相似文献
12.
We obtain sharp estimates for some multilinear commutators related to certain sublinear integral operators. These operators
include the Littlewood-Paley operator and Marcinkiewicz operator. As an application, we obtain weighted L
p
(p > 1) inequalities and an L log L-type estimate for multilinear commutators.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1419–1431, October, 2007. 相似文献
13.
P. Malits 《Acta Appl Math》2007,98(2):135-152
This paper deals with a new class of Fredholm integral equations of the first kind associated with Hankel transforms of integer
order. Analysis of the equations is based on operators transforming Bessel functions of the first kind into kernels of Weber–Orr
integral transforms. Their inverse operators are established by means of new inversion theorems for the Hankel and Weber–Orr
integral transforms of functions belonging to L
1 and L
2. These operators together with the proven Paley–Wiener’s theorem for the Weber–Orr transform enable to regularize the equations
and, in special cases, to derive explicit solutions. The integral equations analyzed in this paper can be employed instead
of dual integral equations usually treated with the Cooke–Lebedev method. An example manifests that it may be preferable because
of the possibility to control norms of operators in the regularized equations.
相似文献
14.
M. Kondo 《Mathematica Slovaca》2011,61(1):1-14
We prove some fundamental properties of monotone modal operators on bounded commutative integral residuated lattices (CRL).
Moreover we give a positive answer to the problem left open in [RACHŮNEK, J.—ŠALOUNOV á, D.: Modal operators on bounded commutative residuated Rℓ-monoids, Math. Slovaca 57 (2007), 321–332]. 相似文献
15.
We prove that the norm of the Euler class E{\mathcal {E}} for flat vector bundles is 2−n
(in even dimension n, since it vanishes in odd dimension). This shows that the Sullivan–Smillie bound considered by Gromov and Ivanov–Turaev is
sharp. In the course of the proof, we construct a new cocycle representing E{\mathcal {E}} and taking only the two values ±2−n
. Furthermore, we establish the uniqueness of a canonical bounded Euler class. 相似文献
16.
Jun Feng LI 《数学学报(英文版)》2005,21(6):1495-1508
In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p(R^n) to L^p(R^n) when the m-th order derivatives of A belong to L^p(R^n) for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are (L^p, L^p)-type operators for 1 〈 p 〈 ∞. 相似文献
17.
Xuan Thinh Duong 《Journal of Functional Analysis》2002,196(2):443-485
We study general spectral multiplier theorems for self-adjoint positive definite operators on L2(X,μ), where X is any open subset of a space of homogeneous type. We show that the sharp Hörmander-type spectral multiplier theorems follow from the appropriate estimates of the L2 norm of the kernel of spectral multipliers and the Gaussian bounds for the corresponding heat kernel. The sharp Hörmander-type spectral multiplier theorems are motivated and connected with sharp estimates for the critical exponent for the Riesz means summability, which we also study here. We discuss several examples, which include sharp spectral multiplier theorems for a class of scattering operators on R3 and new spectral multiplier theorems for the Laguerre and Hermite expansions. 相似文献
18.
In 1934, Whitney raised the question of how to recognize whether a function f defined on a closed subset X of ℝ
n
is the restriction of a function of class 𝒞
p
. A necessary and sufficient criterion was given in the case n=1 by Whitney, using limits of finite differences, and in the case p=1 by Glaeser (1958), using limits of secants. We introduce a necessary geometric criterion, for general n and p, involving limits of finite differences, that we conjecture is sufficient at least if X has a “tame topology”. We prove that, if X is a compact subanalytic set, then there exists q=q
X
(p) such that the criterion of order q implies that f is 𝒞
p
. The result gives a new approach to higher-order tangent bundles (or bundles of differential operators) on singular spaces.
Oblatum 21-XI-2001 & 3-VII-2002?Published online: 8 November 2002
RID="*"
ID="*"Research partially supported by the following grants: E.B. – NSERC OGP0009070, P.M. – NSERC OGP0008949 and the Killam
Foundation, W.P. – KBN 5 PO3A 005 21. 相似文献
19.
Vekua theory for the Helmholtz operator 总被引:1,自引:0,他引:1
A. Moiola R. Hiptmair I. Perugia 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,53(3):779-807
Vekua operators map harmonic functions defined on domain in
\mathbb R2{\mathbb R^{2}} to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original
work of I. Vekua (Ilja Vekua (1907–1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz
equation in a completely explicit fashion, in any space dimension N ≥ 2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they
are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally,
we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results
are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical,
and plane waves. 相似文献
20.
D. A. Labutin 《Mathematical Notes》1997,61(2):164-179
Some classes of cuspidal domainsG ⊂ ℝ
n
are introduced, and embeddings of the formW
p
(l)
(G)↪Lq(G),l ∈ ℕ, for sobolev spaces are established. To this end, estimates of some integral operators are needed. These operators cannot
be estimated via Riesz potentials or their anisotropic analogs.
Translated fromMatematicheskie Zametki, Vol. 61, No. 2, pp. 201–219, February, 1997.
Translated by V. E. Nazaikinskii 相似文献