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1.
This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar's inequality and the sharp maximal function estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained. 相似文献
2.
Self-adjoint quadratic operator pencilsL()=
2
A + B + C with a noninvertible leading operatorA are considered. In particular, a characterization of the spectral points of positive and of negative type ofL is given, and their behavior under a compact perturbation is studied. These results are applied to a pencil arising in magnetohydrodynamics. 相似文献
3.
Double variational principles are established for eigenvalues of a (norm) continuous self-adjoint operator valued functionL defined on a real interval [, [.L() is not required to be definite for any . Applications are made to linear, quadratic and rational functionsL.This author acknowledges support from NSERC of Canada and the I.W. Killam Foundation.This author was supported by the Fonds zur Förderung der wissenschaftlichen Forschung of Austria, Project P 12176-MAT. 相似文献
4.
We show that:(1) For many regular cardinals (in particular, for all successors of singular strong limit cardinals, and for all successors of singular -limits), for all n{2,3,4,...}: There is a linear order L such that L
n
has no (incomparability-)antichain of cardinality , while L
n+1 has an antichain of cardinality .(2) For any nondecreasing sequence
n
:n{2,3,4,...} of infinite cardinals it is consistent that there is a linear order L such that, for all n: L
n
has an antichain of cardinality
n
, but no antichain of cardinality
n
+. 相似文献
5.
We generalize the Ap extrapolation theorem of Rubio de Francia to A∞ weights in the context of Muckenhoupt bases. Our result has several important features. First, it can be used to prove weak endpoint inequalities starting from strong-type inequalities, something which is impossible using the classical result. Second, it provides an alternative to the technique of good-λ inequalities for proving Lp norm inequalities relating operators. Third, it yields vector-valued inequalities without having to use the theory of Banach space valued operators. We give a number of applications to maximal functions, singular integrals, potential operators, commutators, multilinear Calderón-Zygmund operators, and multiparameter fractional integrals. In particular, we give new proofs, which completely avoid the good-λ inequalities, of Coifman's inequality relating singular integrals and the maximal operator, of the Fefferman-Stein inequality relating the maximal operator and the sharp maximal operator, and the Muckenhoupt-Wheeden inequality relating the fractional integral operator and the fractional maximal operator. 相似文献
6.
We consider the Schrödinger operator H in the space $ L_{2}(\mathbb{R}^{d})$ with
a magnetic potential A(x) decaying as $ \vert x\vert^{-1} $ at infinity and satisfying the
transversal gauge condition <A(x), x > = 0. Our goal is to study properties
of the scattering matrix S() associated to the operator H. In particular,
we find the essential spectrum ess of S() in terms of the behaviour of
A(x) at infinity. It turns out that ess(S()) is normally a rich subset of the
unit circle $\mathbb{T}$ or even coincides with $\mathbb{T}$. We find also the diagonal singularity
of the scattering amplitude (of the kernel of S() regarded as an integral
operator). In general, the singular part S0 of the scattering matrix is a sum
of a multiplication operator and of a singular integral operator. However,
if the magnetic field decreases faster than $ \vert x\vert^{-1} $ for d 3 (and the total
magnetic flux is an integer times 2 for dd = 2), then this singular integral
operator disappears. In this case the scattering amplitude has only a weak
singularity (the diagonal Dirac function is neglected) in the forward direction
and hence scattering is essentially of short-range nature. Moreover, we show
that, under such assumptions, the absolutely continuous parts of the operators
S() and S0 are unitarily equivalent. An important point of our approach is
that we consider S() as a pseudodifferential operator on the unit sphere and
find an explicit expression of its principal symbol in terms of A(x). Another
ingredient is an extensive use (for d 3) of a special gauge adapted to a
magnetic potential A(x). 相似文献
7.
A weighted norm inequality for the local sharp maximal function M#
f is proved. Our main result along with the extrapolation theorem by D. Cruz-Uribe and C. Perez is applied
to obtaining several new weighted norm inequalities for maximal functions and singular integrals.
Several open problems are given. 相似文献
8.
We study (s, k, 1, 2)-translation divisible designs with 10 in the singular and semi-regular case. Precisely, we describe singular (s, k, 1, 2)-TDD's by quasi-partitions of suitable quotient groups or subgroups of their translation groups. For semi-regular (s, k, 1, 2)-TDD's (and, more general, for the case 2>1) we prove that their translation groups are either Frobenius groups or p-groups of exponent p. Some examples are given for the singular, semi-regular and regular case. 相似文献
9.
We characterize the relationship between the space L1() and the dual L1() of the space L1(), where (, ) is a dual pair of vector measures with associated spaces of integrable functions L1() and L1() respectively. Since the result is rather restrictive, we introduce the notion of range duality in order to obtain factorizations of operators from Banach function spaces that are dominated by the integration map associated to the vector measure . We obtain in this way a generalization of the Grothendieck-Pietsch Theorem for p-summing operators.*The research was partially supported by MCYT DGI project BFM 2001-2670.**The research was partially supported by MCYT DGI project BFM 2000-1111. 相似文献
10.
Yu L. Shmul'yan 《Mathematical Notes》1969,5(3):212-216
We shall consider holomorphic operator functions F() which have values that differ by a scalar factor from a J-semiunitary operator. We shall establish conditions under which the latter operator is independent of.Translated from Matematicheskie Zametki, Vol. 5, No. 3, pp. 351–359, March, 1969.The author thanks Yu. P, Ginzburg for his discussion of these results. 相似文献
11.
For a comonic polynomialL() and a selfadjoint invertible matrixJ the following two factorization problems are considered: firstly, we parametrize all comonic polynomialsR() such that
. Secondly, if it exists, we give theJ-innerpseudo-outer factorizationL()=()R(), where () isJ-inner andR() is a comonic pseudo-outer polynomial. We shall also consider these problems with additional restrictions on the pole structure and/or zero structure ofR(). The analysis of these problems is based on the solution of a general inverse spectral problem for rational matrix functions, which consists of finding the set of rational matrix functions for which two given pairs are extensions of their pole and zero pair, respectively.The work of this author was supported by the USA-Israel Binational Science Foundation (BSF) Grant no. 9400271. 相似文献
12.
Yuri I. Karlovich Enrique Ramírez de Arellano 《Integral Equations and Operator Theory》2001,39(4):441-474
LetB be the Banach algebra of all bounded linear operators on the weighted Lebesgue spaceL
p (T, ) with an arbitrary Muckenhoupt weight on the unit circleT, and
the Banach subalgebra ofB generated by the operators of multiplication by piecewise continuous coefficients and the operatorse
h,S
T
e
h,
–1
I (hR, T) whereS
T is the Cauchy singular integral operator ande
h,(t)=exp(h(t+)/(t–)),tT. The paper is devoted to a symbol calculus, Fredholm criteria and an index formula for the operators in the algebra
and its matrix analogue
. These shift-invariant algebras arise naturally in studying the algebras of singular integral operators with coefficients admitting semi-almost periodic discontinuities and shifts being diffeomorphisms ofT onto itself with second Taylor derivatives.Partially supported by CONACYT grant, Cátedra Patrimonial, No. 990017-EX and by CONACYT project 32726-E, México. 相似文献
13.
Stephen J. Kirkland Michael Neumann Bryan L. Shader 《Czechoslovak Mathematical Journal》1998,48(1):1-20
Let A be an n × n symmetric, irreducible, and nonnegative matrix whose eigenvalues are 12 ... n. In this paper we derive several lower and upper bounds, in particular on 2 and
n
, but also, indirectly, on
. The bounds are in terms of the diagonal entries of the group generalized inverse, Q
#, of the singular and irreducible M-matrix Q = 1
I – A. Our starting point is a spectral resolution for Q
#. We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected graphs, where now Q becomes L, the Laplacian of the graph. In case the graph is a tree we find a graph-theoretic interpretation for the entries of L
# and we also sharpen an upper bound on the algebraic connectivity of a tree, which is due to Fiedler and which involves only the diagonal entries of L, by exploiting the diagonal entries of L
#. 相似文献
14.
We consider a selfadjoint and smooth enough operator-valued functionL() on the segment [a, b]. LetL(a)0,L(b)0, and there exist two positive numbers and such that the inequality |(L()f, f)|< ([a, b] f=1) implies the inequality (L'()f, f)>. Then the functionL() admits a factorizationL()=M()(I-Z) whereM() is a continuous and invertible on [a, b] operator-valued function, and operatorZ is similar to a selfadjoint one. This result was obtained in the first part of the present paper [10] under a stronge conditionL()0 ( [a,b]). For analytic functionL() the result of this paper was obtained in [13]. 相似文献
15.
Consider a functionL() defined on an interval of the real axis whose values are linear bounded selfadjoint operators in a Hilbert spaceH. A point 0 and a vector
0 H(
0 0) are called eigenvalue and eigenvector ofL() ifL() ifL(0)
0 = 0. Supposing that the functionL() can be represented as an absolutely convergent Fourier integral, the interval is sufficiently small and the derivative will be positive at some point, it has been proved that all the eigenvectors of the operator-functionL() corresponding to the eigenvalues from the interval form an unconditional basis in the subspace spanned by them. 相似文献
16.
Paolo Lipparini 《Archive for Mathematical Logic》1996,35(2):63-87
We develop a method for extending results about ultrafilters into a more general setting. In this paper we shall be mainly concerned with applications to cardinality logics. For example, assumingV=L, Gödel's Axiom of Constructibility, we prove that if > then the logic with the quantifier there exist many is (,)-compact if and only if either is weakly compact or is singular of cofinality<. As a corollary, for every infinite cardinals and , there exists a (,)-compact non-(,)-compact logic if and only if either < orcf<cf or < is weakly compact.Counterexamples are given showing that the above statements may fail, ifV=L is not assumed.However, without special assumptions, analogous results are obtained for the stronger notion of [,]-compactness. 相似文献
17.
In this paper we introduce left linear theories of exponentN (a set) on the setL as mapsL ×L
N
(l, ) l · L such that for alll L and , L
N
the relation (l · ) =l( · ) holds, where · L
N
is given by ( · )(i) = (i),i N. We assume thatL has a unit, that is an element L
N
withl · =l, for alll L, and · = , for all L
N
. Next, left (resp. right)L-modules andL-M-bimodules and their homomorphisms are defined and lead to categoriesL-Mod, Mod-L, andL-M-Mod. These categories are algebraic categories and their free objects are described explicitly. Finally, Hom(X, Y) andX Y are introduced and their properties are investigated.Herrn Professor Dr. D. Pumplün zum 60. Geburtstag gewidmet 相似文献
18.
Let
i(L), i(L*) denote the successive minima of a latticeL and its reciprocal latticeL
*, and let [b1,..., b
n
] be a basis ofL that is reduced in the sense of Korkin and Zolotarev. We prove that and, where and
j denotes Hermite's constant. As a consequence the inequalities are obtained forn7. Given a basisB of a latticeL in
m
of rankn andx
m
, we define polynomial time computable quantities(B) and(x,B) that are lower bounds for 1(L) and(x,L), where(x,L) is the Euclidean distance fromx to the closest vector inL. If in additionB is reciprocal to a Korkin-Zolotarev basis ofL
*, then 1(L)
n
*
(B) and.The research of the second author was supported by NSF contract DMS 87-06176. The research of the third author was performed at the University of California, Berkeley, with support from NSF grant 21823, and at AT&T Bell Laboratories. 相似文献
19.
20.
Michael Sand 《Integral Equations and Operator Theory》1996,26(2):210-221
If is a complex, separable Hilbert space, letL
2 () denote theL
2-space of functions defined on the unit circle and having values in . The bilateral shift onL
2() is the operator (U
f)()=f(). A Hilbert spaceH iscontractively contained in the Hilbert spaceK ifHK and the inclusion mapH–K is a contraction. We describe the structure of those Hilbert spaces, contractively contained inL
2(), that are carried into themselves contractively byU
. We also do this for the subcase of those spaces which are carried into themselves unitarily byU
. 相似文献