Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals

Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.     

Parameterized Littlewood-Paley operators and area integrals on weak hardy spaces

In this paper,we establish the boundedness of parameterized Littlewood-Paley operator μ*,ρλ and parameterized area integral μΩρ,S with kernel satisfying the logarithmic type Lipschitz condition on the weak Hardy space.     

Weighted Hardy spaces in the three-parameter case

In this paper, we use the idea of the discrete Littlewood-Paley theory developed by Han and Lu to carry out the three-parameter weighted Hardy spaces theory under a rather weak condition on the product weight (w∈A_∞) and obtain the boundedness of singular integral operators on the weighted Hardy spaces.     

变量核分数次积分在Hardy空间的有界性

§ 1　 Introduction and main resultsLet Sn- 1 be the unitsphere in Rn(n≥ 2 ) equipped with normalized Lebesgue measure dσ= dσ(z′) .We say that a functionΩ(x,z) defined on Rn× Rnbelongs to L∞ (Rn)× Lr(Sn- 1 )(r≥ 1 ) ,ifΩ(x,z) satisfies the following two conditions,(i) for any x,z∈Rnandλ>0 ,there hasΩ(x,λz) =Ω(x,z) ;(ii)‖Ω‖L∞(Rn)× Lr(Sn- 1) :=supx∈ Rn∫Sn- 1|Ω(x,z′) | rdσ(z′) 1 / r<∞ .For 0 <α相似文献   

SOME MULTIPLIER THEOREMS FOR ANISOTROPIC HARDY SPACES ——In Memory of Professor Yongsheng Sun

Let A be a symmetric expansive matrix and Hp(Rn) be the anisotropic Hardy space associated with A. For a function m in L∞(Rn), an appropriately chosen function η in Cc∞(Rn) and j ∈ Z define mj(ξ) = m(Ajξ)η(ξ). The authors show that if 0 ＜ p ＜ 1 and (m)j belongs to the anisotropic nonhomogeneous Herz space K11/p-1,p(Rn), then m is a Fourier multiplier from Hp(Rn) to Lp(Rn). For p = 1, a similar result is obtained if the space K10,1(Rn) is replaced by a slightly smaller space K(w).Moreover, the authors show that if 0 ＜ p ≤ 1 and if the sequence {(mj)V} belongs to a certain mixednorm space, depending on p, then m is also a Fourier multiplier from Hp(Rn) to Lp(Rn).     

New hardy spaces associated with some anisotropic Herz spaces and their applications

In this paper, a class of anisotropic Herz-type Hardy spaces associated with a non-isotropic dilation on ℝ ⁿ are introduced, and the central atomic and molecular decomposition characterizations of those spaces are established. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy spaces. The research is supported by NSF of China (Grant Nos. 10571014 and 10571015) and SRFDP of China (Grant No. 20050027025)     

Endpoint estimates for Marcinkiewicz integrals on weighted weak hardy spaces

In this paper, we obtain the(W H1ω, W L1ω) type estimate for the Marcinkiewicz integral and the(W H1 b,ω, W L1ω) type estimate for the commutator generated by a BMO function and the Marcinkiewicz integral, where the kernel satisfies a certain logarithmic type Lipschitz condition.     

Nonnegative functions in weighted hardy spaces

Let W be a nonnegative summable function whose logarithm is also summable with respect to the Lebesgue measure on the unit circle. For 0?<?p?<?∞ , H^p (W) denotes a weighted Hardy space on the unit circle. When W?≡?1, H ^p(W) is the usual Hardy space H^p . We are interested in H^p ( W)₊ the set of all nonnegative functions in H^p ( W). If p?≥?1/2, H^p ₊ consists of constant functions. However H^p ( W)₊ contains a nonconstant nonnegative function for some weight W. In this paper, if p?≥?1/2 we determine W and describe H^p ( W)₊ when the linear span of H^p ( W)₊ is of finite dimension. Moreover we show that the linear span of H^p (W)₊ is of infinite dimension for arbitrary weight W when 0?<?p?<?1/2.     

Hardy spaces via distribution spaces

Let ℐ(ℝⁿ) be the Schwartz class on ℝⁿ and ℐ_∞(ℝⁿ) be the collection of functions ϕ ∊ ℐ(ℝⁿ) with additional property that

Boundedness of commutators of generalized fractional integral operators on weighted herz-type hardy spaces

In this paper, we study the boundedness of higher order commutators of generalized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Boundedness of composition operators with mixed homogeneities

Suppose that T₁ is a Calderón–Zygmund operator with isotropic homogeneity and T₂ is a Calderón–Zygmund operator with non‐isotropic homogeneity. In this note, the boundedness of the composition operator on the Hardy space is presented. The results in this paper extend earlier related results on convolution operators to non‐convolution setting.     

Littlewood-Paley inequalities in uniformly convex and uniformly smooth Banach spaces

It is proved that the inequality δX(ε)?cεp, p?2, where δX is the modulus of convexity of X, is sufficient and necessary for the inequality

     

Littlewood-Paley g-函数交换子的Hardy型估计

证明了当q>1时,Littlewood-Paley g-函数与LMO(BMO的一个子空间)函数的交换子g_(Ψ,b)是局部Hardy空间h~1(R~n)到空间h~1(R~n)+L~q(R~n)的一个连续映射.     

The fractional multilinear singular integral with variable kernels on hardy spaces

The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from Lp to Hq.     

Weighted Hardy and singular operators in Morrey spaces

We study the weighted boundedness of the Cauchy singular integral operator SΓ in Morrey spaces Lp,λ(Γ) on curves satisfying the arc-chord condition, for a class of “radial type” almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces Lp,λ(0,?), ?>0. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves.     

Preservers of generalized orthogonality on finite dimensional real vector and projective spaces

We describe the general form of bijective orthogonality preserving maps on ? ⁿ equipped with a pair of generalized indefinite inner products. The relations between the projective space and vector space versions of this result are examined and an example is given showing that the hypotheses of our main theorem are essential.     

Outer operators for the noncommutative symmetric hardy spaces associated with finite subdiagonal algebra

In this article, we extended main results on outer operators of [6] to the symmetric Hardy spaces, when associated subdiagonal algebra is finite.