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1.
Estimates of Marcinkiewicz Integrals with Bounded Homogeneous Kernels of Degree Zero 总被引:2,自引:0,他引:2
Under the cancellation property and a certain Dini-type condition
on kernels, we prove that Marcinkiewicz integrals with kernels which are homogeneous
functions of degree zero, are bounded from
to
,
from
to
, and from
to
for
. 相似文献
3.
Let B(H) denote the algebra of operators on a complex Hilbert
space H, and let U denote the class of operators
which satisfy
the absolute value condition
.
It is proved that if
is a
contraction, then either A has a nontrivial invariant subspace or A is a proper
contraction and the nonnegative operator
is strongly stable. A Putnam-Fuglede type commutativity theorem is proved for contractions A in
,
and it is shown that if normal subspaces of
. It is proved that if
are reducing, then every compact operator in the intersection of the weak closure of the range of the
derivation
with the commutant of A* is quasinilpotent. 相似文献
4.
Consider the Schrödinger operator
with a complex-valued
potential v of period
Let
and
be the eigenvalues of L that are close to
respectively, with periodic (for n even),
antiperiodic (for n odd), and Dirichelet
boundary conditions on [0,1], and let
be the diameter of the spectral
triangle with vertices
We prove the following statement: If
then v(x) is a Gevrey function, and moreover
相似文献
5.
6.
To every egglike inversive plane
there is associated a family
of involutions of the point set of
such that
circles of
are the fixed point sets of the involutions in
. Korchmaros and Olanda characterized a family
of involutions on a set of size n2 + 1to be
for
an egglike inversive plane of order n by four conditions. In this
paper, we give an alternative proof where the Galois space PG(3,n) in
which
is embedded is built up directly by using concepts and
results on finite linear spaces. 相似文献
7.
In this paper, we obtain a sufficient condition for two-weight weak
type norm inequality for the commutators of fractional integral
,
where
and
. 相似文献
8.
We investigate the ideal structure of the Toeplitz algebra
of a totally ordered abelian group
. We show that the primitive ideals of
are parametrised by the disjoint union
of the duals
of the order ideals
of
, and identify the
hull-kernel topology on
when the chain of orderideals in
is isomorphic to a subset of
相似文献
9.
The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. 相似文献
10.
The oblique derivative problem for the Laplace equation is studied
in a planar multiply connected domain. The boundary condition has a form
where
is the unit normal vector,
is the unit tangential
vector and
is a fixed real number. If
is a Hölderian function and the
corresponding domain has Ljapunov boundary then the classical problem is
studied. If
on the boundary and the domain has a locally Lipschitz
boundary then a solution, which fulfils the boundary condition in the sense of
a nontangential limit, is studied. If
is a real measure on the boundary and the
domain has bounded cyclic variation then a solution in a sense of distributions
is studied. The solution is looked for in a form of a linear combination of a
single layer potential and an angular potential. 相似文献
11.
In this note we examine the relationships between p-hyponormal
operators and the operator inequality
. This leads to a method for
generating examples of p-hyponormal operators which are not q-hyponormal
for any
. Our methods are also shown to have implications for the class
of Furuta type inequalities. 相似文献
12.
An Operator Transform from Class A to the Class of Hyponormal Operators and its Application 总被引:1,自引:0,他引:1
In this paper, we shall give an operator transform
from class A to the class of hyponormal operators. Then we shall show that
and
in case T belongs to class A. Next, as an application of
we will show that every class A operator has SVEP and property (β). 相似文献
13.
The goal of this paper is to extend some previous results on abelian ideals of Borel subalgebras to so-called spherical ideals of
These are ideals
of
such that their G-saturation
is a spherical G-variety. We classify all maximal spherical ideals of
for all simple G.Received: 25 March 2004 相似文献
14.
The aim of this paper is to prove two perturbation results for a selfadjoint operator A in a Krein space
which can roughly be described as follows: (1) If is an open subset of
and all spectral subspaces for A corresponding to compact subsets of have finite rank of negativity, the same is true for a selfadjoint operator B in
for which the difference of the resolvents of A and B is compact. (2) The property that there exists some neighbourhood of such that the restriction of A to a spectral subspace for A corresponding to is a nonnegative operator in
is preserved under relative
perturbations in form sense if the resulting operator is again selfadjoint. The assertion (1) is proved for selfadjoint relations A and B. (1) and (2) generalize some known results. 相似文献
15.
In this note we prove the uniqueness of U in a group G with
a spherical split-BN-pair of rank
,i.e., if G has such a BN-pair with
a nilpotent normal subgroup of B,
and
, then
and
is a normal subgroup of G. Here
is the corresponding group of Lie-type and
the subgroup of
generated by all root-subgroups corresponding to positive roots.
Received: 19 May 2003 相似文献
16.
We consider the three-dimensional Schrödinger operators
and
where
, A is a magnetic potential generating a constant magnetic
field of strength
, and
where
decays fast enough at infinity. Then, A. Pushnitskis representation of the spectral shift function (SSF)
for the pair of operators
is well defined for energies
We study the behaviour of the associated representative of the equivalence class
determined by the SSF, in a neighbourhood of the Landau levels
Reducing our analysis to the study of the eigenvalue asymptotics for a family of
compact operators of Toeplitz type, we establish a relation between the type of the
singularities of the SSF at the Landau levels and the decay rate of V at infinity.
Communicated by Bernard HelfferSubmitted 23/09/03, accepted 15/01/04 相似文献
17.
Daoxing Xia 《Integral Equations and Operator Theory》2006,55(3):439-452
This paper studies pure subnormal k-tuples of operators
with finite rank of self-commutators. It determines the substantial part of the conjugate of the joint point spectrum of
which is the union of domains in Riemann surfaces in some algebraic varieties in
The concrete form of the principal current [4] related to
is also determined. Besides, some operator identities are found for
相似文献
18.
Let be a Radon measure on
which may be non-doubling. The only condition that must satisfy is
for all
and for some fixed
In this paper, under this assumption, the Lp()-boundedness (1 < p < ) and certain weak type endpoint estimate are established for multilinear commutators, which are generated by Calderón-Zygmund singular integrals with RBMO() functions or with
functions for r 1, where
is a space of Orlicz type satisfying that
if r = 1 and
if r > 1. 相似文献
19.
In the canonical smooth fiber bundles
endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups
and construct
-invariant generalizations of differentiable connections. In both regular and special cases of the representations of the relevant groups
, we found all the affine nonholonomic
-,
-, and
-connections of the first order (see [1]–[3]) possessing the local Lie groups of transformations
and also described the respective
-invariant planar connections. 相似文献
20.
A. M. Protopopov 《Algebra and Logic》2003,42(4):279-286
We study into the question of whether a partial order can be induced from a partially right-ordered group
onto a space
of right cosets of
w.r.t. some subgroup
of
. Examples are constructed showing that the condition of being convex for
in
is insufficient for this. A necessary and sufficient condition (in terms of a subgroup
and a positive cone
of
) is specified under which an order of
can be induced onto
. Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups
for which
is partially ordered for every convex subgroup
, and properties of the class of groups such that
is partially ordered for every partial right order
on
and every subgroup
that is convex under
. 相似文献