Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several cla...The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators.展开更多
In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimens...In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.展开更多
Let p is an element of (n/(n + 1), 1]. The authors investigate the (H-b(p)(R-n), L-p(R-n))-type and (H-b(p,infinity)(R-n), L-p,L-infinity(R-n))-type continuities for the maximal operators associated with the commutato...Let p is an element of (n/(n + 1), 1]. The authors investigate the (H-b(p)(R-n), L-p(R-n))-type and (H-b(p,infinity)(R-n), L-p,L-infinity(R-n))-type continuities for the maximal operators associated with the commutators of Bochner-Riesz operators with BMO(R-n) functions, where H-b(p)(R-n) and H-b(p,infinity)(R-n) are, respectively, the variants of the standard Hardy spaces and the standard weak Hardy spaces.展开更多
Our aim in the present paper is to prove the boundedness of commutators on Morrey spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.
For Banach space-valued martingale, two new BMO spaces, namely BMO (X), resp-BMO (X), and two new sharp operators, namely, resp. generated by the condition-al p-mean-square resp. p-mean-square operator are introduce...For Banach space-valued martingale, two new BMO spaces, namely BMO (X), resp-BMO (X), and two new sharp operators, namely, resp. generated by the condition-al p-mean-square resp. p-mean-square operator are introduced, and then, the connections betweenBMO (X) and BMO;, BMO(X) and BMO and and are investigated. The resultsobtained here yield a new charactrization of the convexity and smoothness of Banach space.展开更多
Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a func...Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a function b ∈ BMO （X）,the commutator [b,T] （f）=T （b f）- bT （f） is bounded on spaces L^p for all p, 1 〈 p 〈 ∞.展开更多
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 var...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.展开更多
The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces
In this note, the author prove that maximal Bocher-Riesz commutator Bδ,＊^b generated by operator Bδ,＊ and function b∈ BMO（ω） is a bounded operator from L^p（μ） into L^p（ν）, where w∈ （μν^- 1）^1/p,μ...In this note, the author prove that maximal Bocher-Riesz commutator Bδ,＊^b generated by operator Bδ,＊ and function b∈ BMO（ω） is a bounded operator from L^p（μ） into L^p（ν）, where w∈ （μν^- 1）^1/p,μ,v ∈ Ap for 1 〈 p 〈 ∞. The proof relies heavily on the pointwise estimates for the sharp maximal function of the commutator Bδ,＊^b.展开更多
For an analytic function f on the hyperbolic domain Ω in C,the following conclusions are obtained: (i)f∈B(Ω)=BMOA(Ω,m)if and only if Ref∈B(?)(Ω)=BMOH(Ω,m).(ii)QB_h(Ω)=B_h(Ω) (BMOH,(Ω,m)=BMOH(Ω,m)if and only...For an analytic function f on the hyperbolic domain Ω in C,the following conclusions are obtained: (i)f∈B(Ω)=BMOA(Ω,m)if and only if Ref∈B(?)(Ω)=BMOH(Ω,m).(ii)QB_h(Ω)=B_h(Ω) (BMOH,(Ω,m)=BMOH(Ω,m)if and only if C(Ω)=inf{Z_o(z)·δ_o(z)·z≡Ω}>0,Also some applica- lions to automorphic function are considered.展开更多
目的:通过航天诱变选育优良的知母突变体,定向培育成药用部分品质提升的优良种质资源。方法:利用我国发射的神舟三号宇宙飞船搭载知母种子,回收后在地面上筛选繁育,并对枝叶和产量等方面占优势的第4代太空组及地面组知母药用部分中多种...目的:通过航天诱变选育优良的知母突变体,定向培育成药用部分品质提升的优良种质资源。方法:利用我国发射的神舟三号宇宙飞船搭载知母种子,回收后在地面上筛选繁育,并对枝叶和产量等方面占优势的第4代太空组及地面组知母药用部分中多种元素含量用 X 射线荧光光谱(XRF)和粉末 X 射线衍射(PXRD)法测定并对比分析。结果:太空知母元素种类无改变,但 Zn、Sr 元素含量比地面组知母分别提高到2.7和1.7倍,Al 元素含量降低66.7%;并首次用 PXRD 技术在知母中鉴别出一水草酸钙晶体,太空知母中该晶体含量和晶粒尺寸比地面组明显减小。结论:航天诱变第4代知母中一水草酸钙晶体的含量明显减少,微量元素指标明显优化。通过航天诱变育种可以筛选出品质优化的知母新品种。展开更多
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
文摘The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators.
基金partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0018)partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0019)+1 种基金by the grant of Science Development Foundation under the President of the Republic of Azerbaijan project EIF-2010-1(1)-40/06-1partially supported by the Scientific and Technological Research Council of Turkey(TUBITAK Project No:110T695)
文摘In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.
基金Tang Lin and Yang Dachun are supported in part by the NNSF and the SEDF of China.
文摘Let p is an element of (n/(n + 1), 1]. The authors investigate the (H-b(p)(R-n), L-p(R-n))-type and (H-b(p,infinity)(R-n), L-p,L-infinity(R-n))-type continuities for the maximal operators associated with the commutators of Bochner-Riesz operators with BMO(R-n) functions, where H-b(p)(R-n) and H-b(p,infinity)(R-n) are, respectively, the variants of the standard Hardy spaces and the standard weak Hardy spaces.
基金supported by NSFC (No. 11101001 and No. 11201003)Education Committee of Anhui Province (No. KJ2011A138 and No. KJ2012A133)
文摘Our aim in the present paper is to prove the boundedness of commutators on Morrey spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.
文摘For Banach space-valued martingale, two new BMO spaces, namely BMO (X), resp-BMO (X), and two new sharp operators, namely, resp. generated by the condition-al p-mean-square resp. p-mean-square operator are introduced, and then, the connections betweenBMO (X) and BMO;, BMO(X) and BMO and and are investigated. The resultsobtained here yield a new charactrization of the convexity and smoothness of Banach space.
基金Supported by the National Natural Science Foundation of China
文摘Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a function b ∈ BMO （X）,the commutator [b,T] （f）=T （b f）- bT （f） is bounded on spaces L^p for all p, 1 〈 p 〈 ∞.
文摘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.
基金supported by the NSF(11271175) of Chinathe NSF(ZR2012AQ026) of Shandong Province
文摘The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces
基金supported by the NNSF (10961015, 11261023) of Chinathe Jiangxi Natural Science Foundation of China (20122BAB201011), GJJ12203
文摘In this note, the author prove that maximal Bocher-Riesz commutator Bδ,＊^b generated by operator Bδ,＊ and function b∈ BMO（ω） is a bounded operator from L^p（μ） into L^p（ν）, where w∈ （μν^- 1）^1/p,μ,v ∈ Ap for 1 〈 p 〈 ∞. The proof relies heavily on the pointwise estimates for the sharp maximal function of the commutator Bδ,＊^b.
基金This research was supported by the Doctoral Program Foundation of Institute of Higher Education.
文摘For an analytic function f on the hyperbolic domain Ω in C,the following conclusions are obtained: (i)f∈B(Ω)=BMOA(Ω,m)if and only if Ref∈B(?)(Ω)=BMOH(Ω,m).(ii)QB_h(Ω)=B_h(Ω) (BMOH,(Ω,m)=BMOH(Ω,m)if and only if C(Ω)=inf{Z_o(z)·δ_o(z)·z≡Ω}>0,Also some applica- lions to automorphic function are considered.
文摘目的:通过航天诱变选育优良的知母突变体,定向培育成药用部分品质提升的优良种质资源。方法:利用我国发射的神舟三号宇宙飞船搭载知母种子,回收后在地面上筛选繁育,并对枝叶和产量等方面占优势的第4代太空组及地面组知母药用部分中多种元素含量用 X 射线荧光光谱(XRF)和粉末 X 射线衍射(PXRD)法测定并对比分析。结果:太空知母元素种类无改变,但 Zn、Sr 元素含量比地面组知母分别提高到2.7和1.7倍,Al 元素含量降低66.7%;并首次用 PXRD 技术在知母中鉴别出一水草酸钙晶体,太空知母中该晶体含量和晶粒尺寸比地面组明显减小。结论:航天诱变第4代知母中一水草酸钙晶体的含量明显减少,微量元素指标明显优化。通过航天诱变育种可以筛选出品质优化的知母新品种。
