Boundedness of Caldero'n-Zygmund operators in product Hardy spaces

By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.

THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERóN-ZYGMUND OPERATORS

Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(x,·)being an Orlicz function andφ(·,t)being a Muckenhoupt A∞(A)weight.In this paper,our goal is to study two boundedness theorems for commutators of anisotropic Calderon-Zygmund operators.Precisely,when b∈BMOw(R^n,A)(a proper subspace of anisotropic bounded mean oscillation space BMO(R^n,A)),the commutator[b,T]is bounded from anisotropic weighted Hardy space H^1ω(R^n,A)to weighted Lebesgue space L^1ω(R^n)and when b∈BMO(R^n)(bounded mean oscillation space),the commutator[b,T]is bounded on Musielak-Orlicz space L^φ(R^n),which are extensions of the isotropic setting.

CALDER6N-ZYGMUND OPERAORS ON THE HARDY SPACES OF WEIGHTED HERZ TYPE

Applying the decomposition theorems in [1] and [2] , we obtain the boundedness theorem of Calderbn-Zygmund operator of type 6 on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear operators on the weighted Herz spaces. -

Multilinear Calderón-Zygmund Operators and Their Commutators with BMO Functions in Herz-Morrey Spaces with Variable Smoothness and Integrability

In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.

Weak Type Weighted Inequalities for the Commutators of the Multilinear Calderón-Zygmund Operators

For the commutators of multilinear Calder ′on-Zygmund singular integral operators with B MO functions, the weak type weighted norm inequalities with respect to A^P weights are obtained.

Boundedness for Commutators of Calderón-Zygmund Operator on Herz-Type Hardy Space with Variable Exponent

Our aim in this paper is to prove the boundedness of commutators of Calderón-Zygmund operator with the Lipschitz function or BOM function on Herz-type Hardy space with variable exponent.

Boundedness of Calderón-Zygmund Operator and Their Commutator on Herz Spaces with Variable Exponent

The aim of this paper is to study the boundedness of Calderón-Zygmund operator and their commutator on Herz Spaces with two variable exponents p(.),q(.). By applying the properties of the Lebesgue spaces with variable exponent, the boundedness of the Calderón-Zygmund operator and the commutator generated by BMO function and Calderón-Zygmund operator is obtained on Herz space.

WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS

In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ （1,∞）, p_2,…,p_m ∈（1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1（R n,M_l（logL） σw）× p2（Rn,M~w）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p_1 and the order of commutator

Composition of Maximal Operators on Space of Homogeneous Type

Let Φ be a Young function and MΦ be the maximal operator associated with Φ in the space of homogeneous type.In this paper,the composition of the maximal operators of type MΦ is considered,and the result established by Carrozza and Passarelli Di Napoli[2] is generalized to the space of homogeneous type.

ESTIMATES FOR THE MAXIMAL MULTILINEAR SINGULAR INTEGRAL OPERATORS

In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the L^P（R^n） （1 〈 p 〈 ∞） boundedness and a weak type LlogL estimate for the corresponding maximal operator.

一类Calderón-Zygmund算子在Besov空间上的连续性(英文)

In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B 0,q p (1 ≤ p, q ≤∞), which is mainly dependent on the properties of the Daubechies wavelets and Lemari's T1 theorem for Besov spaces.

Boundedness of Rough Operators on Grand Variable Herz Spaces

In this paper, we prove the boundedness of Calderón-Zygmund singular integral operators TΩ on grand Herz spaces with variable exponent under some conditions.

Calderón-Zygmund-Type Operators on Weighted Weak Hardy Spaces over R^n

We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted Lebesgue spaces,weighted weak Lebesgue spaces,weighted Hardy spaces and weighted weak Hardy spaces.The sharpness of some results is also investigated.

Toeplitz operators related to strongly singular Calderón-Zygmund operators

In this paper, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderón-Zygmund operators and Lipschitz function b ∈(Λ)β0(Rn) is discussed from Lp(Rn) to Lq(Rn),1/q=1/p-β0/n, and from Lp(Rn) to Triebel-Lizorkin space (F)β0,∞p. We also obtain the boundedness of generalized Toeplitz operator Θbα0 from Lp(Rn) to Lq(Rn), 1/q=1/p-α0+β0/n.All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on Lp(Rn), 1 ＜ p ＜ ∞ .

Weighted norm inequalities for the multilinear Calderón-Zygmund operators

In this paper, by proving some suitable weighted endpoint estimates, and then by multilinear interpolation and a new multilinear extrapolation lemma, the author establishes some weighted estimates for the multilinear Calderón-Zygmund operator. Also, the author gives a weighted estimate for the corresponding commutator.

Weak Hardy-type spaces associated with ball quasi-Banach function spaces I:Decompositions with applications to boundedness of Calderón-Zygmund operators

Let X be a ball quasi-Banach function space on R^(n).In this article,we introduce the weak Hardytype space WH_(X)(R^(n)),associated with X,via the radial maximal function.Assuming that the powered HardyLittlewood maximal operator satisfies some Fefferman-Stein vector-valued maximal inequality on X as well as it is bounded on both the weak ball quasi-Banach function space WX and the associated space,we then establish several real-variable characterizations of WH_(X)(R^(n)),respectively,in terms of various maximal functions,atoms and molecules.As an application,we obtain the boundedness of Calderón-Zygmund operators from the Hardy space H_(X)(R^(n))to WH_(X)(Rn),which includes the critical case.All these results are of wide applications.Particularly,when X:=M^(q)_(p)(R^(n))(the Morrey space),X:=L^(p)(R^(n))(the mixed-norm Lebesgue space)and X:=(EΦq)t(Rn)(the Orlicz-slice space),which are all ball quasi-Banach function spaces rather than quasiBanach function spaces,all these results are even new.Due to the generality,more applications of these results are predictable.

Boundedness of Vector Valued Bilinear Calderón-Zygmund Operators on Products of Weighted Herz-Morrey Spaces with Variable Exponents

In this paper,the authors obtain the boundedness of vector valued bilinear Calderón-Zygmund operators on products of weighted Herz-Morrey spaces with variable exponents.

Θ-type Calderón-Zygmund Operators with Non-doubling Measures

Let μ be a Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ（B（x,r）） ≤ Urn for all x∈Rd, r 〉 0 and for some fixed 0 〈 n 〈 d. In this paper, under this assumption, we prove that 0-type Calder6n-Zygmund operator which is bounded on L2 （μ） is also bounded from L^∞（μ） into RBMO （μ） and from Hb （μ） into L1（μ）. According to the interpolation theorem introduced by Tolsa, the LP（μ）-boundedness （1 〈 p 〈 ∞） is established for θ-type Calder6n-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type CMderθn-Zygmundoperator with RBMO （μ） function are bounded on LP（μ） （1 〈 p 〈 ∞）.

Boundedness of Commutators of θ-Type Calderón-Zygmund Operators on Non-homogeneous Metric Measure Spaces

Let(X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hyt?nen. In this paper, the authors obtain the boundedness of the commutators of θ-type Calderón-Zygmund operators with RBMO functions from L∞(μ) into RBMO(μ) and from Hat1,∞(μ) into L1(μ), respectively.As a consequence of these results, they establish the Lp(μ) boundedness of the commutators on the non-homogeneous metric spaces.

Weighted estimates for iterated commutators of multilinear Calderón-Zygmund operators on non-homogeneous metric measure spaces

Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-doubling measure as special cases. Let T be a multilinear Calderón-Zygmund operator and b:=(b1,..., bm) be a finite family of RBMO(μ) functions. In this paper, some weak-type multiple weighted estimates for the iterated commutator T∏bgenerated by T and b are obtained.