具有非倍测度的Marcinkiewicz积分交换子的有界性

证明了具有非倍测度的Marcinkiewicz积分交换子Mb具有(Lp(μ),Lq(μ))有界性,同时也是(L1(μ),Lq,∞(μ))有界.此外,证明了Mb不仅是(Lp(μ),Lip(β-n/p))有界,而且还是(Ln/β(μ),RBMO(μ))的有界算子.     

双线性Fourier乘子交换子的有界性与紧性

假定T_σ是关于乘子σ的双线性Fourier乘子算子,其中σ满足如下Sobolev正则条件:对某个s∈(n,2n],有sup_(κ∈Z)‖σ_k‖W~s(R~(2m))∞.对于p_1,p_2,p∈(1,∞)且满足1/p=1/p_1+1/p_2和ω=(ω_1,ω_2)∈A_(p/t)(R~(2n)),建立了T_σ及其与函数b=(b_1,b_2)∈(BMO(R~n))~2生成的交换子T_(σ,b)由L~(p_1,λ)(ω_1)×L~(p_2,λ)(ω_2)到L~(p,λ)(v_w)的有界性;同时,在b_1,b_2∈CMO(R~n)(C_c~∞(R~n)在BMO拓扑下的闭包)的条件下,证明交换子T_(σ,b)是L~(p_1,λ)(ω_1)×L~(p_2,λ)(ω_2)到L~(p,λ)(v_w)的紧算子.为了得到主要结果,我们先后建立了几个双(次)线性极大函数在加多权Morrey空间上的有界性以及该空间中准紧集的判定.     

振荡超奇性Hilbert变换的Sobolev有界性

主要研究R~n上沿曲线Γ(t)=(t~(p_1),t~(p_2),…,t~(p_n))的振荡超奇性Hilbert变换H_(n,α,β)=∫_0~1 f(x-Γ(t))e~(it-β)t~(-1-α),在Sobolev空间上的有界性,其中0p_1P_2…P_n,αβ0.证明了对于0γ(nα)/((n+1))(p_1+α),当|1/p-1/2|(β-(n+1)[α-(β+p_1)γ])/(2β)时,H_(n,α,β)是从L_γ~2(R~n))到L~2(R~n)的有界算子.特别地,当β≥(α-γp_1)/(γ+1/(n+1))等时,H_(n,α,β)是从L_γ~2(R~n)到L~2(R~n)的有界算子·     

与强奇异Calderón-Zygmund算子相关的Toeplitz型算子

研究与强奇异Calderón-Zygmund算子和Lipschitz函数6∈ΛA_(βO)(R~n)相关的Toeplitz型算子T_b(f)从L~p(R~n)到L~q(R~n)的有界性和L~p(R~n)到Triebel- Lizorkin空间F(_p~(βO,∞))的有界性,1／q=1／p-βO／n．得到广义Toeplitz型算子Θ(_(αO)~b)是L~p(R~n)到L~q(R~n)有界的,1／q=1／p-(αO βO)／n．上述结果包含相应交换子的有界性．同时还得到与强奇异Calderón-Zygmund算子和BMO函数b相关的Toeplitz型算子T_b(f)的L~p(R~n)有界性,1＜p＜∞.     

乘子与Herz型空间

通过某些加权或非加权的Herz空间,将关于乘子算子有界性的H\"{o}rmander条件用一个更弱的条件来替代,并建立起乘子算子的一些有界性结果. 作为文中主要定理的直接推论,一些关于乘子算子有界性的著名结果得到了改进或者直接导出.     

带多项式相位的高维振荡积分算子的有界性

考虑如下的振荡积分算子:T_(m,k,n)f(x):=∫_(R~n)e~(i(x_1~2+…+x_n~2))~m(y_1~2+…+y_n~2)~kf(y)dy,其中函数f为定义在R~n上的Schwartz函数,并且满足m,k0.本文给出算子T_(m,k,n).从L~p(R~n)(1≤p∞)到L~q(R~n)有界的一个充分必要条件.此外,我们还证明了算子T_(m,k,n)把L~1(R~n)映到C_0(R~n).     

R~n上一类高阶奇异Teodorescu算子的性质

讨论了R~n上的一类高阶奇异Teodorescu算子的有界性.首先定义了一类R~n上的高阶T算子,然后将算子分为两部分,并且利用Hlder不等式及一些引理证明了该算子在整个R~n上的一致有界性.     

从Hardy空间到Bers型空间的微分算子与乘子的积

给定复平面中单位圆盘D上的全纯自映射ψ(z),讨论了Hardy空间和Bers型空间之间的微分算子与乘子的积DM_ψ的有界性和紧性,得到了若干充要条件.     

广义Fock空间上的Hankel算子

利用有界(消失)平均振荡函数的性质,本文刻画了一类广义Fock空间上的Hankel算子的有界性(紧性),同时,还刻画了换位子[M_f,P]的有界性和紧性,其中P是一个Toeplitz投影算子,而M_f表示符号为f的乘子.最后,应用Berezin变换来研究了BMO空间和VMO空间的几何性质.     

非倍测度下Marcinkiewicz积分交换子在Hardy空间中的有界性

在测度μ仅满足多项式增长性条件的假设下,证明了Marcinkiewicz积分算子M与Lipβ(μ)函数b生成的交换子Mb具有(H1(μ), Ln/(n?β)(μ))有界性,同时得到Mb的(Ln/β(μ), RBMO(μ))有界性.     

满足H(m)条件的奇异积分算子的交换子的有界性

主要讨论了满足H(m)条件的奇异积分算子与Lipschitz函数的交换子在L~p和Hardy空间的有界性,并把这个结果应用于与薛定谔算子相关的Riesz变换.     

Toeplitz operators related to strongly singular Calderón-Zygmund operators

In this paper, the boundedness of Toeplitz operator T _b(f) related to strongly singular Calderón-Zygmund operators and Lipschitz function b ε (ℝⁿ) is discussed from L ^p(ℝⁿ) to L ^q(ℝⁿ), , and from L ^p(ℝⁿ) to Triebel-Lizorkin space . We also obtain the boundedness of generalized Toeplitz operator Θ _α0 ^b from L ^p(ℝⁿ) to L ^q(ℝⁿ), . All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator T _b(f) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on L ^p(ℝⁿ), 1 < p < ∞.     

Some estimates of maximal commutators for Bochner-Riesz operator on Morrey spaces

In this note, the authors show the boundedness of the maximal commutators of Bocher-Riesz operator B ^δ and that of maximal commutator B _δ1* ^b generated by B ^δ and a Lipschitz function b mapping from M _p ^q (R ⁿ ) into BMO space and also maps from M _p ^q (R ⁿ ) into L _(β−n/q).     

Interpolation theorems for variable exponent Lebesgue spaces

When Hardy-Littlewood maximal operator is bounded on Lp(⋅)(Rn) space we prove θ[Lp(⋅)(Rn),BMO(Rn)]=Lq(⋅)(Rn) where q(⋅)=p(⋅)/(1−θ) and θ[Lp(⋅)(Rn),H¹(Rn)]=Lq(⋅)(Rn) where 1/q(⋅)=θ+(1−θ)/p(⋅).     

ON MULTILINEAR COMMUTATORS OF Θ-TYPE CALDERóN-ZYGMUND OPERATORS

In this paper, we discuss the multilinear commutator of θ-type Calderón- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from Lp(Rn) to Lq(Rn), from Lp(Rn) to Triebel-Lizorkin spaces and on certain Hardy type spaces.     

The weighted Herz-type Hardy spaces hK q α,p (ω1,ω2)

Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω₁,ω₂ ɛA ₁(R ⁿ ) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk _q ^α,p (gw₁,ω₂) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R ⁿ ), the class of C^∞(Rⁿ)-functions with compactly support, is dense inhK _q ^α,p (ω₁,ω₂) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK _q ^α,p (ω₁,ω₂), of any bounded sequence inhK _q ^α,p (ω₁,ω₂). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness. Supported by the NECF and the NECF and the NNSF of China.     

Boundedness of commutators on homogeneous Morrey-Herz spaces over locally compact Vilenkin groups

This paper studies some boundedness results of commutators on a class of new spaces M K˙pα,,qλ (G) named as homogenous Morrey-Herz spaces over locally compact Vilenkin groups.     

Average Width and Optimal Interpolation of the Sobolev-Wiener Class Wpq(R) in the Metric Lq(R)

In this paper, we determine the exact value of average n − K width _n(W^r_pq(R), L_q(R)) of Sobolev-Wiener class W^r_pq(R) in the metric L_q(R) for 1 > q ≥ p > ∞ and get the value of _n(W^r_p(R), L_qp(R)) for the dual case. We also solve the optimal interpolation problems of W^r_pq(R) in the metric L_q(R) and W^r_p(R) in the metric L_qp(R) for 1 < q ≤ p < ∞.     

Higher order commutators for a class of rough operators

In this paper we study the (L ^p (u ^p ),L ^q (v ^q )) boundedness of the higher order commutatorsT _Ω,α,b ^m andM _Ω,α,b ^m formed by the fractional integral operatorT _Ω,α , the fractional maximal operatorM _Ω,α , and a functionb(x) in BMO(v), respectively. Our results imporve and extend the corresponding results obtained by Segovia and Torrea in 1993 [9]. The project was supported by NNSF of China.     

Boundedness of maximal,potential type,and singular integral operators in the generalized variable exponent Morrey type spaces

We consider generalized Morrey type spaces M^{p( ·),q( ·),w( ·)}( W) {\mathcal{M}^{p\left( \cdot \right),\theta \left( \cdot \right),\omega \left( \cdot \right)}}\left( \Omega \right) with variable exponents p(x), θ(r) and a general function ω(x, r) defining a Morrey type norm. In the case of bounded sets W ì \mathbbRⁿ \Omega \subset {\mathbb{R}^n} , we prove the boundedness of the Hardy–Littlewood maximal operator and Calderón–Zygmund singular integral operators with standard kernel. We prove a Sobolev–Adams type embedding theorem M^{p( ·),q₁( ·),w₁( ·)}( W) ? M^{q( ·),q₂( ·),w₂( ·)}( W) {\mathcal{M}^{p\left( \cdot \right),{\theta_1}\left( \cdot \right),{\omega_1}\left( \cdot \right)}}\left( \Omega \right) \to {\mathcal{M}^{q\left( \cdot \right),{\theta_2}\left( \cdot \right),{\omega_2}\left( \cdot \right)}}\left( \Omega \right) for the potential type operator I ^α(·) of variable order. In all the cases, we do not impose any monotonicity type conditions on ω(x, r) with respect to r. Bibliography: 40 titles.