共查询到20条相似文献,搜索用时 11 毫秒
1.
The exact bounds are obtained for the norm of the singular integral operator S on the family of rays originating at the same point. These bounds, with the use of the localization technique, are then extended
to the essential norm of S on piecewise smooth curves with finitely many points of self intersection.
Submitted: April 13, 2007. Accepted: September 19, 2007. 相似文献
2.
We establish a new calculus of pseudodifferential operators on a manifold with smooth edges and study ellipticity with extra
trace and potential conditions (as well as Green operators) at the edge. In contrast to the known scenario with conditions
of that kind in integral form we admit in this paper ‘singular’ trace and Green operators. In contrast to standard conditions
in the theory of elliptic boundary value problems (like Dirichlet or Neumann conditions) our singular trace conditions, in
general, do not act on functions that are smooth up to the boundary, but admit a more general asymptotic structure. Their
action is now associated with the Laurent coefficients of the meromorphic Mellin transforms of functions with respect to the
half-axis variable, the distance to the edge. 相似文献
3.
Shuichi Sato 《Integral Equations and Operator Theory》2008,62(3):429-440
We prove certain L
p
-estimates for Littlewood-Paley functions arising from rough kernels. The estimates are useful for extrapolation to prove
L
p
-boundedness of the Littlewood-Paley functions under a sharp kernel condition.
相似文献
4.
David Eelbode 《Advances in Applied Clifford Algebras》2007,17(4):635-649
We introduce a framework for studying differential operators which are invariant with respect to the real (complex) symplectic
Lie algebra
(
), associated to a quaternionic structure on a vector space
. To do so, these algebras are realized within the orthogonal Lie algebra
. This leads in a natural way to a refinement of the recently introduced notion of complex Hermitean Clifford analysis, in
which four variations of the classical Dirac operator play a dominant role.
David Eelbode: Postdoctoral fellow supported by the F.W.O. Vlaanderen (Belgium). 相似文献
5.
In this paper the authors give the boundedness of the commutator of Marcinkiewicz integral with rough variable kernel, which is an extension of the result in
[5] .
Research supported by NSF of China (Grant: 10571015) and SRFDP of China (Grant: 20050027025). 相似文献
6.
S. P. Eveson 《Integral Equations and Operator Theory》2008,62(4):585-589
We show that if V
α (α > 0) is the Riemann-Liouville fractional integration operator and T is an invertible operator on L
2(0, 1) which commutes with V , then TV
α is not supercyclic on L
2(0, 1); in particular, many Volterra convolution operators are not supercyclic. The technique is based on an argument used
by Gallardo-Gutiérrez and Montes-Rodríguez to show that V is not supercyclic. 相似文献
7.
Let (X, ~) be a combinatorial graph the vertex set X of which is a discrete metric space. We suppose that a discrete group G acts freely on (X, ~) and that the fundamental domain with respect to the action of G contains only a finite set of points. A graph with these properties is called periodic with respect to the group G. We examine the Fredholm property and the essential spectrum of band-dominated operators acting on the spaces l
p
(X) or c_0(X), where (X, ~) is a periodic graph. Our approach is based on the thorough use of band-dominated operators. It generalizes the necessary
and sufficient results obtained in [39] in the special case and in [42] in case X = G is a general finitely generated discrete group.
Submitted: May 21, 2007. Revised: September 25, 2007. Accepted: November 5, 2007. 相似文献
8.
Hiroyuki Chihara 《Integral Equations and Operator Theory》2009,63(3):321-335
We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex
n-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sj?strand. We also obtain
the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order
three are in the Wiener algebra of Sj?strand. Our method of proofs is based on the pseudodifferential calculus and the heat
flow determined by the phase function of the Bargmann transform.
Supported by the JSPS Grant-in-Aid for Scientific Research #20540151. 相似文献
9.
Fabrizio Colombo Irene Sabadini Daniele C. Struppa 《Advances in Applied Clifford Algebras》2009,19(2):225-236
We employ the notion of slice monogenic functions to define a new functional calculus for an n-tuple of not necessarily commuting operators. This calculus is consistent with the Riesz-Dunford calculus for a single operator.
Received: October, 2007. Accepted: February, 2008. 相似文献
10.
This paper studies the connection between an analytic function φ on the unit disk and a certain type of operators induced by φ on weighted Bergman spaces A
α of analytic functions on . The general theme is the interplay between smoothness conditions on φ and the S
p
-norms of the operators induced by φ.
相似文献
11.
Let b be a BMO function, and the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) for the operator and for the pairs of weights of the type (w, ), where w is any weight and is a suitable one-sided maximal operator. We also prove that, for weights, the operator is controlled in the L
p
(w) norm by a composition of the one-sided fractional maximal operator and the one-sided Hardy-Littlewood maximal operator iterated
k times. These results improve those obtained by an immediate application of the corresponding two-sided results and provide
a different way to obtain known results about the operators . The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral
This research has been partially supported by Spanish goverment Grant MTM2005-8350-C03-02. The first author was also supported
by CONICET, ANPCyT and CAI+D-UNL. The second author was also supported by Junta de Andalucía Grant FQM 354. 相似文献
12.
Let J
α
k
be a real power of the integration operator J
k
defined on the Sobolev space W
k
p
[0, 1]. We investigate the spectral properties of the operator defined on . Namely, we describe the commutant {A
k
}′, the double commutant and the algebra Alg
A
k
. Moreover, we describe the lattices Lat
A
k
and HypLat
A
k
of invariant and hyperinvariant subspaces of A
k
, respectively. We also calculate the spectral multiplicity of A
k
and describe the set Cyc
A
k
of its cyclic subspaces. In passing, we present a simple counterexample for the implication
to be valid.
相似文献
13.
Viorel Catană 《Integral Equations and Operator Theory》2008,62(3):351-363
We define two-wavelet localization operators in the setting of homogeneous spaces. We prove that they are in the trace class
S
1 and give a trace formula for them. Then we show that two-wavelet operators on locally compact and Hausdorff groups endowed
with unitary and square-integrable representations, general Daubechies operators and two-wavelet multipliers can be seen as
two-wavelet localization operators on appropriate homogeneous spaces. Thus we give a unifying view concerning the three classes
of linear operators. We also show that two-wavelet localization operators on , considered as a homogeneous space, under the action of the affine group U are two-wavelet multipliers
相似文献
14.
Trieu Le 《Integral Equations and Operator Theory》2009,63(4):547-555
For any α > −1, let A2α be the weighted Bergman space on the unit ball corresponding to the weight (1 – |z|2)α. We show that if all except possibly one of the Toeplitz operators are diagonal with respect to the standard orthonormal basis of A2α and has finite rank, then one of the functions must be the zero function.
相似文献
15.
We study finite rank semicommutators and commutators of Toeplitz operators on the Bergman space with quasihomogeneous symbols.
We show that in this context, the situation is different from the case of harmonic Toeplitz operators.
Submitted: July 23, 2007. Accepted: December 4, 2007. 相似文献
16.
The classical Fischer decomposition of polynomials on Euclidean space makes it possible to express any polynomial as a sum
of harmonic polynomials multiplied by powers of |x|2. A deformation of the Laplace operator was recently introduced by Ch.F. Dunkl. It has the property that the symmetry with
respect to the orthogonal group is broken to a finite subgroup generated by reflections (a Coxeter group). It was shown by
B. ?rsted and S. Ben Said that there is a deformation of the Fischer decomposition for polynomials with respect to the Dunkl
harmonic functions. In Clifford analysis, a Dunkl version of the Dirac operator was introduced and studied by P. Cerejeiras,
U. K?hler and G. Ren. The aim of the article is to describe an analogue of the Fischer decomposition for solutions of the
Dunkl Dirac operator. The main methods used are coming from representation theory, in particular, from ideas connected with
Howe dual pairs.
This paper is dedicated to the memory of our friend and colleague Jarolim Bureš to recall our long lasting cooperation on
many topics in mathematics
The work presented here is a part of the research project MSM 0021620839 and was supported also by the grant GA ČR 201/05/2117.
Received: October, 2007. Accepted: February, 2008. 相似文献
17.
Nicolas Th. Varopoulos 《Milan Journal of Mathematics》2008,76(1):419-429
In this note I give an extension of the T1-Theorem of David and Journé. In this extension the standard estimates on the kernel
are replaced by “average standard estimates” but the classical proof is essentially identical. I then use that extension to
prove the Lp-boundedness of some natural rough singular integrals. The applications of these singular integrals in Potential Theory has
already been described in my previous paper in the area.
Received: September 2008 相似文献
18.
M. E. Luna-Elizarrarás M. A. Macías-Cedeño M. Shapiro 《Advances in Applied Clifford Algebras》2009,19(2):375-390
In a previous paper we introduced the concept of a two-dimensional directional derivative of a quaternionic function along
a two-dimensional plane. In this paper we provide a deeper analysis of its properties, as well as of its relations with hyperholomorphic
functions, with holomorphic maps of two complex variables and with Cullen-regular functions.
Received: October, 2007. Accepted: February, 2008. 相似文献
19.
The necessary and sufficient conditions of Fredholmness and the index formula for a boundary value problems for a pair of
polyanalytic functions, containing differential operators as well as operators with Carleman shift and conjugations, are obtained.
Submitted: May 16, 2007. Accepted: November 5, 2007. 相似文献
20.
We introduce non-linear Dirac operators in associated to the p-harmonic equation and we extend to other contexts including spin manifolds and the sphere.
This paper is dedicated to the memory of Jarolim Bureš
Received: October, 2007. Accepted: February, 2008. 相似文献