Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain cri...Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N（X） and Na（X） if and only if it is weakly compact on the vector-valued Hardy space H^1 （X） and Bergman space B1（X） respectively.展开更多
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 i...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.展开更多
Let G be a locally compact Vilenkin gro up . We will establish the boundedness in Morrey spaces L p,λ (G) for a la rge class of sublinear operators and linear commutators.
In this paper some new results concerning the C_p classes introduced by Muckenhoupt(1981)and later extended by Sawyer(1983),are provided.In particular,we extend the result to the full expected range p>0,to the weak...In this paper some new results concerning the C_p classes introduced by Muckenhoupt(1981)and later extended by Sawyer(1983),are provided.In particular,we extend the result to the full expected range p>0,to the weak norm,to other operators and to their vector-valued extensions.Some of those results rely upon sparse domination,which in the vector-valued case are provided as well.We will also provide sharp weighted estimates for vector-valued extensions relying on those sparse domination results.展开更多
This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operator...This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operators and fractional integral operators with homogeneous kernels on block-type spaces.展开更多
We prove some boundedness results for a large class of sublinear operators with rough kernel on the homogeneous Herz spaces where the three main indices are variable exponents.Some known results are extended.
文摘Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N（X） and Na（X） if and only if it is weakly compact on the vector-valued Hardy space H^1 （X） and Bergman space B1（X） respectively.
基金supported by the National Natural Science Foundation of China(10871025)
文摘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.
文摘Let G be a locally compact Vilenkin gro up . We will establish the boundedness in Morrey spaces L p,λ (G) for a la rge class of sublinear operators and linear commutators.
基金supported by the Basque Government through the Basque Excellence Research Centre 2018–2021 ProgramAgencia Estatal de Investigacion/European Regional Development Fund of UE(Grant No.MTM 2017-82160-C2-1-P),Acronym“Harmonic Analysis and Quantum Mechanics”+4 种基金Spanish Ministry of Economy and Competitiveness through Basque Center for Applied Mathematics Severo Ochoa Excellence Accreditation(Grant No.SEV-2013-0323)Universidad Nacional del Sur(Grant No.11/X752)Agencia Nacional de Promocion Cientifica y Tecnologica of Argentina(Grant No.PICT 2014-1771)Juan de la Cierva-Formacion2015(Grant No.FJCI-2015-24547)Consejo Nacional de Investigaciones Cientificas y Tecnicas/Proyectos de Investigacion Plurianuales of Argentina(Grant No.11220130100329CO)。
文摘In this paper some new results concerning the C_p classes introduced by Muckenhoupt(1981)and later extended by Sawyer(1983),are provided.In particular,we extend the result to the full expected range p>0,to the weak norm,to other operators and to their vector-valued extensions.Some of those results rely upon sparse domination,which in the vector-valued case are provided as well.We will also provide sharp weighted estimates for vector-valued extensions relying on those sparse domination results.
文摘This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operators and fractional integral operators with homogeneous kernels on block-type spaces.
基金Natural Science Foundation of Education Committee of Anhui Province(No.KJ2019A1196)Anhui Provincial Natural Science Foundation(No.1908085MA19)Preresearch Project of the NNSF of China(No.2019yyzrl4).
文摘We prove some boundedness results for a large class of sublinear operators with rough kernel on the homogeneous Herz spaces where the three main indices are variable exponents.Some known results are extended.
