Continuity properties for commutators of multilinear type operators on product of certain Hardy spaces

Similar to the property of a linear Calderdn-Zygmund operator, a linear fractional type operator Is associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ≤ 1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b,Iα] is continuous from an atomic Hardy space Hp b into Lp, where Hp b is a subspace of the Hardy space Hp for n/（n ＋ 1） 〈 p ≤ 1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint （Hp1 b1 ×... × HP2, Lp） boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderdn-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b ∈ （Lipβ）m（Rn）.     

Bochner-Riesz算子的多线性交换子的有界性

In this paper,the boundedness for the multilinear commutators of Bochner-Riesz operator is considered.We prove that the multilinear commutators generated by Bochner-Riesz operator and Lipschitz function are bounded from Lp（Rn）into ∧˙（β-np）（Rn）and from Lnβ（Rn）into BMO（Rn）.     

Boundedness of multilinear operators on generalized Morrey spaces

In this paper, the authors prove the boundedness of the multilinear maximal functions, multilinear singular integrals and multilinear Riesz potential on the product generalized Morrey spaces Mp1,ω1(Rn) ×···× Mpm,ω1(Rn) respectivelyThe main theorems of this paper extend some known results.     

Boundedness of parabolic singular integrals and Marcinkiewicz integrals on Triebel-Lizorkin spaces

In this paper,we obtain the boundedness of the parabolic singular integral operator T with kernel in L(logL)1/γ(Sn-1) on Triebel-Lizorkin spaces.Moreover,we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q(f) from ∥f∥ F˙p0,q(Rn) into Lp(Rn).     

Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces

Let L be the infinitesimal generator of an analytic semigroup on L2 (Rn) with Gaussian kernel bound, and let L-α/2 be the fractional integrals of L for 0<α相似文献   

LIPSCHITZ ESTIMATES FOR MULTILINEAR SINGULAR INTEGRALS,Ⅱ

In this paper, the authors study two classes of multilinear singular integrals and obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herz type spaces to central Campanato spaces. Moreover, the authors also consider the extreme cases.     

LIPSCHITZ ESTIMATES FOR MULTILINEAR SINGULAR INTEGRALS, II

In this paper, the authors study two classes of multilinear singular integralsand obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herztype spaces to central Campanato spaces. Moreover, the authors also consider the extremecases.     

Orlicz-Hardy spaces and their duals

We establish the theory of Orlicz-Hardy spaces generated by a wide class of functions.The class will be wider than the class of all the N-functions.In particular,we consider the non-smooth atomic decomposition.The relation between Orlicz-Hardy spaces and their duals is also studied.As an application,duality of Hardy spaces with variable exponents is revisited.This work is different from earlier works about Orlicz-Hardy spaces H(Rn)in that the class of admissible functions is largely widened.We can deal with,for example,(r)≡(rp1(log(e+1/r))q1,0r 6 1,rp2(log(e+r))q2,r1,with p1,p2∈(0,∞)and q1,q2∈(.∞,∞),where we shall establish the boundedness of the Riesz transforms on H(Rn).In particular,is neither convex nor concave when 0p11p2∞,0p21p1∞or p1=p2=1 and q1,q20.If(r)≡r(log(e+r))q,then H(Rn)=H(logH)q(Rn).We shall also establish the boundedness of the fractional integral operators I of order∈(0,∞).For example,I is shown to be bounded from H(logH)1./n(Rn)to Ln/(n.)(log L)(Rn)for 0n.     

Boundedness of Multilinear Caldern–Zygmund Singular Operators on Morrey–Herz Spaces with Variable Exponents

In this paper,we introduce Morrey–Herz spaces M K˙(·)q,p(·)(Rn) with variable exponents α(·) and p(·),and prove the boundedness of multilinear Caldern–Zygmund singular operators on the product of these spaces.     

Toeplitz operators related to strongly singular Calderón-Zygmund operators

In this paper, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and Lipschitz function b∈Λβ0(Rn) is discussed from Lp(Rn) to Lq(Rn), 1/q=1/p-β0/n, and from Lp(Rn) to Triebel-Lizorkin space Fβ0,∞p. We also obtain the boundedness of generalized Toeplitz operatorθbα0 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 Calderon-Zygmund operators and BMO function b is discussed on LP(Rn), 1 < p <∞.     

Multilinear Calderón-Zygmund Operator on Products of Hardy Spaces

In this paper, the authors establish the boundedness of the multilinear Calderón-Zygmund operator from products of Hardy spaces into Hardy spaces.     

Multi-parameter hardy spaces via discrete Littlewood-Paley theory

In this paper, we apply a discrete Littlewood-Paley analysis to obtain Hardy spaces HP(Rn× ......× Rnk) of arbitrary number of parameters characterized by discrete Littlewood-Paley square function and derive the boundedness of singular integral operators on HP(Rn1×......×Rnk) and from HP(Rn1×......× Rnk) to LP(Rn1×......× Rnk).     

Commutator of hypersingular integral with rough kernels on Sobolev spaces

In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ (Rn) to the Lebesgue space Lp(Rn) for 1p∞ and 0 γ min{ n/2 , n/p }.     

Weak Morrey spaces and strong solutions to the Navier-Stokes equations

We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p ＞ 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1＜p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results.     

SOME ENDPOINT ESTIMATES FOR COMMUTATORS OF θ-TYPE CALDERóN-ZYGMUND OPERATORS

In this note, the authors prove that the commutator Tb generated by θ-type Calderón-Zygmund operator T and a Lipschitz function b is bounded from Lp(Rn) into Lip(β- np)(Rn) and also maps from L βn (Rn) into BMO(Rn).     

Some Oscillatory Singular Integrals on Herz-type Spaces (Ⅱ)

In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the Lebesgue spaceL1(Rn).     

CBMO estimates for multilinear Hardy operators

The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, the Herz spaces and the Morrey-Herz spaces.     

A note on the generalized Marcinkiewicz integral operators with rough kernels

In this paper,we study the generalized Marcinkiewicz integral operators MΩ,r on the product space Rn×Rm.Under the condition that Ω is a function in certain block spaces,which is optimal in some senses,the boundedness of such operators from Triebel-Lizorkin spaces to Lp spaces is obtained.     

Multilinear Fractional Integrals and Commutators on Generalized Herz Spaces

Suppose b =(b_1, ···, b_m) ∈(BMO)~m, I_(α,m)~(Πb) is the iterated commutator of b and the m-linear multilinear fractional integral operator I_(α,m). The purpose of this paper is to discuss the boundedness properties of I_(α,m) and I_(α,m)~(Πb) on generalized Herz spaces with general Muckenhoupt weights.     

Extension of isometries on the unit sphere of L p spaces

In this paper we study the isometric extension problem and show that every surjective isometry between the unit spheres of Lp (μ) (1 p ∞, p≠2) and a Banach space E can be extended to a linear isometry from Lp(μ) onto E, which means that if the unit sphere of E is (metrically) isometric to the unit sphere of Lp(μ), then E is linearly isometric to Lp(μ). We also prove that every surjective 1-Lipschitz or anti-1-Lipschitz map between the unit spheres of Lp (μ1, H1) and Lp(μ2,H2) must be an isometry and can be extended to a linear isometry from Lp (μ1,H1) to Lp (μ2,H2), where H1 and H2 are Hilbert spaces.