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1.
We study the maximal and fractional maximal functions and Riesz potentials that are generated by the generalized shift operator associated with the Laplace-Bessel operator. We obtain some pointwise and integral estimates that give a relation between the B-maximal and B-fractional maximal functions and B-Riesz potentials and extend the available results to the objects of a more general nature. Basing on these results, we prove interpolation theorems for the B-fractional maximal functions and B-Riesz potentials. 相似文献
2.
In this paper we prove the O’Neil inequality for the k-linear convolution f ⊗ g. By using the O’Neil inequality for rearrangements we obtain a pointwise rearrangement estimate of the k-linear convolution. As an application, we obtain necessary and sufficient conditions on the parameters for the boundedness
of the k-sublinear fractional maximal operator M
Ω, α and k-linear fractional integral operator I
Ω, α with rough kernels from the spaces
V.S. Guliyev partially supported by the grant of INTAS (project 05-1000008-8157). 相似文献
3.
We introduce operators of q-fractional integration through inverses of the Askey–Wilson operator and use them to introduce a q-fractional calculus. We establish the semigroup property for fractional integrals and fractional derivatives. We study properties of the kernel of q-fractional integral and show how they give rise to a q-analogue of Bernoulli polynomials, which are now polynomials of two variables, x and y. As q→1 the polynomials become polynomials in x−y, a convolution kernel in one variable. We also evaluate explicitly a related kernel of a right inverse of the Askey–Wilson operator on an L2 space weighted by the weight function of the Askey–Wilson polynomials. 相似文献
4.
We study the
boundedness of generalized multilinear fractional integrals. An O’Neil type inequality for a k-linear integral operator is proved. Using an O’Neil type inequality for a k-linear integral operator, we obtain a pointwise rearrangement estimate of generalized multilinear fractional integrals. By
way of application we prove a Sobolev type theorem for these integrals.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 3, pp. 577–585, May–June, 2007. 相似文献
5.
Vagif S. Guliyev Ayhan Serbetci Ismail Ekincioglu 《Journal of Mathematical Analysis and Applications》2007,336(1):425-437
In this paper, the necessary and sufficient conditions are found for the boundedness of the rough B-fractional integral operators from the Lorentz spaces Lp,s,γ to Lq,r,γ, 1<p<q<∞, 1?r?s?∞, and from L1,r,γ to Lq,∞,γ≡WLq,γ, 1<q<∞, 1?r?∞. As a consequence of this, the same results are given for the fractional B-maximal operator and B-Riesz potential. 相似文献
6.
S. Mecheri 《Czechoslovak Mathematical Journal》2007,57(2):697-703
Let ℋ be a separable infinite dimensional complex Hilbert space, and let ℒ(H) denote the algebra of all bounded linear operators on ℋ into itself. Let A = (A
1, A
2,..., A
n), B = (B
1, B
2,..., B
n) be n-tuples of operators in ℒ(H); we define the elementary operators Δ
A,B
: ℒ(H) ↦ ℒ(H) by
.
In this paper, we characterize the class of pairs of operators A, B ∈ ℒ(H) satisfying Putnam-Fuglede’s property, i.e, the class of pairs of operators A,B ∈ ℒ(H) such that
implies
for all T ∈ C
1 (H) (trace class operators). The main result is the equivalence between this property and the fact that the ultraweak closure
of the range of the elementary operator ΔA,B is closed under taking adjoints. This leads us to give a new characterization of the orthogonality (in the sense of Birkhoff)
of the range of an elementary operator and its kernel in C
1 classes.
This work was supported by the research center project No. 2005-04. 相似文献
7.
Sebastian Król 《Semigroup Forum》2009,79(2):369-376
We show that every contractive C
0-semigroup on a separable, infinite-dimensional Hilbert space X can be approximated by unitary C
0-groups in the weak operator topology uniformly on compact subsets of ℝ+. As a consequence we get a new characterization of a bounded H
∞-calculus for the negatives of generators of bounded holomorphic semigroups. Applications of our results to the study of a
topological structure of the set of (almost) weakly stable contractive C
0-semigroups on X are also discussed.
The author was partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”, and by a MNiSzW
grant Nr. N201384834. 相似文献
8.
In this paper, we study closed k-maximal spacelike hypersurfaces M
n
in anti-de Sitter space H
1
n+1 (−1) with two distinct principal curvatures and give some integral formulas about these hypersurfaces.
The first author was supported by Japan Society for Promotion of Science. The third author was supported by grant Proj. No.
R17-2008-001-01000-0 from Korea Science & Engineering Foundation. 相似文献
9.
Vagif S. Guliyev Javanshir J. Hasanov 《Journal of Mathematical Analysis and Applications》2008,347(1):113-122
We consider the generalized shift operator, associated with the Laplace-Bessel differential operator . The maximal operator Mγ (B-maximal operator) and the Riesz potential (B-Riesz potential), associated with the generalized shift operator are investigated. At first, we prove that the B-maximal operator Mγ is bounded from the B-Morrey space Lp,λ,γ to Lp,λ,γ for all 1<p<∞ and 0?λ<n+|γ|. We prove that the B-Riesz potential , 0<α<n+|γ| is bounded from the B-Morrey space Lp,λ,γ to Lq,λ,γ if and only if α/(n+|γ|−λ)=1/p−1/q, 1<p<(n+|γ|−λ)/α. Also we prove that the B-Riesz potential is bounded from the B-Morrey space L1,λ,γ to the weak B-Morrey space WLq,λ,γ if and only if α/(n+|γ|−λ)=1−1/q. 相似文献
10.
We study the Riesz potentials that are generated by the generalized shift operator associated to the Laplace-Bessel operator. We obtain an analog of the Sobolev-Il’in theorem for the B-Riesz potential. 相似文献
11.
In this note,we prove that the Toeplitz-type Operator Θ b α generated by the generalized fractional integral,Calderón-Zygmund operator and VMO funtion is bounded from L p,λ (R n) to L q,μ (R n).We also show that under some conditions Θαb f ∈ V L q,μ (B R),the vanishing-Morrey space. 相似文献
12.
On the Equivalence and Generalized of Weyl Theorem Weyl Theorem 总被引:3,自引:0,他引:3
M. BERKANI 《数学学报(英文版)》2007,23(1):103-110
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a sinlilar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators. 相似文献
13.
Kewei Zhang 《Frontiers of Mathematics in China》2008,3(4):599-642
We study the ‘universal’ strong coercivity problem for variational integrals of degenerate p-Laplacian type by mixing finitely many homogenous systems. We establish the equivalence between universal p-coercivity and a generalized notion of p-quasiconvex extreme points. We then give sufficient conditions and counterexamples for universal coercivity. In the case
of noncoercive systems we give examples showing that the corresponding variational integral may have infinitely many non-trivial
minimizers in W
01,p
which are nowhere C
1 on their supports. We also give examples of universally p-coercive variational integrals in W
01,p
for p ⩾ with L
∞ coefficients for which uniqueminimizers under affine boundary conditions are nowhere C
1.
相似文献
14.
D. H. Yuan X. L. Liu A. Chinchuluun Graduate Student P. M. Pardalos 《Journal of Optimization Theory and Applications》2006,129(1):185-199
In this paper, we present necessary optimality conditions for nondifferentiable minimax fractional programming problems. A
new concept of generalized convexity, called (C, α, ρ, d)-convexity, is introduced. We establish also sufficient optimality conditions for nondifferentiable minimax fractional programming
problems from the viewpoint of the new generalized convexity. When the sufficient conditions are utilized, the corresponding
duality theorems are derived for two types of dual programs.
This research was partially supported by NSF and Air Force grants 相似文献
15.
We obtain optimal bounds of order O(n
−1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution
functions of random matrices from the GUE and LUE, respectively.
Research supported by the DFG-Forschergruppe FOR 399/1. Partially supported by INTAS grant N 03-51-5018, by RFBR grant N 02-01-00233,
and by RFBR-DFG grant N 04-01-04000. 相似文献
16.
The paper studies the first homology of finite regular branched coverings of a universal Borromean orbifold called B
4,4,4ℍ3. We investigate the irreducible components of the first homology as a representation space of the finite covering transformation
group G. This gives information on the first betti number of finite coverings of general 3-manifolds by the universality of B
4,4,4. The main result of the paper is a criterion in terms of the irreducible character whether a given irreducible representation
of G is an irreducible component of the first homology when G admits certain symmetries. As a special case of the motivating argument the criterion is applied to principal congruence
subgroups of B
4,4,4. The group theoretic computation shows that most of the, possibly nonprincipal, congruence subgroups are of positive first
Betti number.
This work is partially supported by the Sonderforschungsbereich 288. 相似文献
17.
Suppose that E and F are two Banach spaces and that B(E, F) is the space of all bounded linear operators from E to F. Let T
0∈B(E, F) with a generalized inverse T
0
+∈B(F, E). This paper shows that, for every T∈B(E, F) with ‖T
0
+ (T−T
0)‖<1, B ≡ (I + T
0
+(T−T
0))−1
T
0
+ is a generalized inverse of T if and only if (I−T
0
+
T
0)N(T) = N(T
0), where N(·) stands for the null space of the operator inside the parenthesis. This result improves a useful theorem of Nashed and
Cheng and further shows that a lemma given by Nashed and Cheng is valid in the case where T
0 is a semi-Fredholm operator but not in general. 相似文献
18.
This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K
0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X
2 is not a sufficient condition of K
0(B(X)) = 0. 相似文献
19.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(4):1099-1105
A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element.
This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002.
The work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information
(grant I/2/2005). 相似文献
20.
Composition Operators on the Bloch Space of Several Complex Variables 总被引:19,自引:0,他引:19
Abstract
In this paper, we study the boundedness and compactness of composition operator C
φ on the Bloch space β(Ω), Ω being a bounded homogeneous domain. For Ω = B
n, we give the necessary and sufficient conditions for a composition operator C
φ to be compact on β(B
n) or β
0(B
n).
Supported by the National Natural Science Foundation and the National Education Committee Doctoral
Foundation 相似文献