共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller than the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón-Zygmund type and to build a theory of weights adapted to the multilinear setting. A natural variant of the operator which is useful to control certain commutators of multilinear Calderón-Zygmund operators with BMO functions is then considered. The optimal range of strong type estimates, a sharp end-point estimate, and weighted norm inequalities involving both the classical Muckenhoupt weights and the new multilinear ones are also obtained for the commutators. 相似文献
3.
Miloud Assal 《Journal of Computational and Applied Mathematics》2009,233(3):617-620
In this paper we consider the generalized shift operator generated from the Laguerre hypergroup; by means of this, pseudo-differential operators are investigated and Sobolev-boundedness results are obtained. 相似文献
4.
In this paper we give sufficient conditions to imply
the $H^{1}_{w}-L^{1}_{w}$ boundedness of the Marcinkiewicz
integral operator $\mu_\Omega$, where w
is a Muckenhoupt weight. We also prove that, under the stronger condition
$\Omega \in {\rm Lip}_\alpha$, the operator $\mu_\Omega$ is bounded from
$H^{p}_{w}$ to $L^{p}_{w}$ for $\max\{n/(n+1/2), n/(n+\alpha)\}$ < p < 1. 相似文献
5.
The Continuity of Commutators on Triebel-Lizorkin Spaces 总被引:6,自引:0,他引:6
The purpose of this paper is to study the continuity in the context of
Triebel-Lizorkin spaces for some commutators related to certain convolution
operators. The operators include Littlewood-Paley operator, Marcinkiewicz
integral and Bochner-Riesz operator. 相似文献
6.
L. Ephremidze 《Georgian Mathematical Journal》1996,3(1):49-52
The uniqueness theorem for the one-sided maximal operator has been proved. 相似文献
7.
We prove Lp boundedness for the maximal operator of the heat semigroup associated to the Laguerre functions, , when the parameter α is greater than -1. Namely, the maximal operator is of strong type (p,p) if p>1 and , when -1<α<0. If α?0 there is strong type for 1<p?∞. The behavior at the end points is studied in detail. 相似文献
8.
James E. Daly 《Journal of Fourier Analysis and Applications》1999,5(4):303-308
Calderón-Zygmund singular integral operators have been extensively studied for almost half a century. This paper provides a context for and proof of the following result: If a Calderón-Zygmund convolution singular integral operator is bounded on the Hardy space H1 (Rn), then the homogeneous of degree zero kernel is in the Hardy space H1(Sn–1) on the sphere. 相似文献
9.
Andrei K. Lerner 《Archiv der Mathematik》2005,85(6):538-543
We show that the Hardy-Littlewood maximal operator and a class of Calderón-Zygmund singular integrals satisfy the strong type
modular inequality in variable Lp spaces if and only if the variable exponent p(x) ∼ const.
Received: 15 September 2004 相似文献
10.
Viktor I. Burenkov Huseyn V. Guliyev Vagif S. Guliyev 《Journal of Computational and Applied Mathematics》2007
The problem of the boundedness of the fractional maximal operator Mα, 0<α<n, in local and global Morrey-type spaces is reduced to the problem of the boundedness of the Hardy operator in weighted Lp-spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for the boundedness for all admissible values of the parameters. Moreover, in case of local Morrey-type spaces, for some values of the parameters, these sufficient conditions coincide with the necessary ones. 相似文献
11.
This article proves the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem
establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly
at its vertex. It thus unifies earlier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilbert
transform of Lacey-Thiele, where the multiplier is not smooth. Using a Whitney decomposition in the Fourier plane, a general
bilinear operator is represented as infinite discrete sums of time-frequency paraproducts obtained by associating wave-packets
with tiles in phase-plane. Boundedness for the general bilinear operator then follows once the corresponding Lp-boundedness of time-frequency paraproducts has been established. The latter result is the main theorem proved in Part in
Part II, our subsequent article [11], using phase-plane analysis.
In memory of A.P. Calderón 相似文献
12.
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
13.
Tengizi S. Kopaliani 《Positivity》2006,10(3):467-474
Let X be a Banach function space, L∞ [0, 1] ⊂ X ⊂ L1[0, 1]. It is proved that if dual space of X has singularity property in closed set E ⊂ [0, 1] then: 1) there exists no orthonormal basis in C[0, 1], which forms an unconditional basis in X in metric of L1[0, 1] space, 2) for the Hardy-Littlewood maximal operator M we have 相似文献
14.
Kamal El Fahri 《Quaestiones Mathematicae》2016,39(4):487-496
We investigate Banach lattices on which each positive almost Dunford- Pettis operator is almost limited and conversely. 相似文献
15.
In this paper we construct a positive doubly power bounded operator
with a nonpositive inverse on an AL-space. 相似文献
16.
Let (Rn,|⋅|,dγ) be the Gauss measure metric space, where Rn denotes the n-dimensional Euclidean space, |⋅| the Euclidean norm and for all x∈Rn the Gauss measure. In this paper, for any a∈(0,∞), the authors introduce some BLOa(γ) space, namely, the space of functions with bounded lower oscillation associated with a given class of admissible balls with parameter a. Then the authors prove that the noncentered local natural Hardy–Littlewood maximal operator is bounded from BMO(γ) of Mauceri and Meda to BLOa(γ). Moreover, a characterization of the space BLOa(γ), via the local natural maximal operator and BMO(γ), is given. The authors further prove that a class of maximal singular integrals, including the corresponding maximal operators of both imaginary powers of the Ornstein–Uhlenbeck operator and Riesz transforms of any order associated with the Ornstein–Uhlenbeck operator, are bounded from L∞(γ) to BLOa(γ). 相似文献
17.
Joonil Kim 《Mathematische Zeitschrift》2008,258(2):271-290
Let {X
j
, Y
j
, T : 1 ≤ j ≤ n} be a basis satisfying the commutation relation for the Heisenberg Lie algebra . Then we obtain a multi-parameter Marcinkiewicz multiplier theorem for the operator defined by m(X
1,..., X
n
, Y
1,..., Y
n
, T). 相似文献
18.
Antonios D. Melas 《Advances in Mathematics》2005,192(2):310-340
For each p>1 we precisely evaluate the main Bellman functions associated with the dyadic maximal operator on and the dyadic Carleson imbedding theorem. Actually, we do that in the more general setting of tree-like maximal operators. These provide refinements of the sharp Lp inequalities for those operators. For this we introduce an effective linearization for such maximal operators on an adequate set of functions. 相似文献
19.
Na Cheng 《Quaestiones Mathematicae》2018,41(6):839-845
We show that for positive operator B : E → E on Banach lattices, if there exists a positive operator S : E → E such that:1.SB ≤ BS;2.S is quasinilpotent at some x0 > 0; 3.S dominates a non-zero b-AM-compact operator, then B has a non-trivial closed invariant subspace. Also, we prove that for two commuting non-zero positive operators on Banach lattices, if one of them is quasinilpotent at a non-zero positive vector and the other dominates a non-zero b-AM-compact operator, then both of them have a common non-trivial closed invariant ideal. Then we introduce the class of b-AM-compact-friendly operators and show that a non-zero positive b-AM- compact-friendly operator which is quasinilpotent at some x0 > 0 has a non-trivial closed invariant ideal. 相似文献
20.
The boundedness of maximal Bochner-Riesz operator Bδ* and that of maximal commutator Bδb,* generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space are established. 相似文献