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
In this paper, the author studies the mapping properties for some general maximal op- erators and singular integrals on certain function spaces via Fourier transform estimates. Also, some concrete maximal operators an...In this paper, the author studies the mapping properties for some general maximal op- erators and singular integrals on certain function spaces via Fourier transform estimates. Also, some concrete maximal operators and singular integrals are studied as applications.展开更多
The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of subline...The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.展开更多
We introduce a class of generalized Orlicz-type Auscher-Mourgoglou slice space,which is a special case of the Wiener amalgam.We prove versions of the Rubio de Francia extrapolation theorem in this space.As a consequen...We introduce a class of generalized Orlicz-type Auscher-Mourgoglou slice space,which is a special case of the Wiener amalgam.We prove versions of the Rubio de Francia extrapolation theorem in this space.As a consequence,we obtain the boundedness results for several classical operators,such as the Calderón-Zygmund operator,the Marcinkiewicz integrals,the Bochner-Riesz means and the Riesz potential,as well as variational inequalities for differential operators and singular integrals.As an application,we obtain global regularity estimates for solutions of non-divergence elliptic equations on generalized Orlicz-type slice spaces if the coefficient matrix is symmetric,uniformly elliptic and has a small(δ,R)-BMO norm for some positive numbers δ and R.展开更多
We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type （1, 1） inequalities. As an application, we prove th...We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type （1, 1） inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension.展开更多
The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral...The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.展开更多
We prove the boundedness from Lp（T2） to itself, 1 〈 p 〈∞, of highly oscillatory singular integrals Sf（x, y） presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of in...We prove the boundedness from Lp（T2） to itself, 1 〈 p 〈∞, of highly oscillatory singular integrals Sf（x, y） presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of integration, roughly speaking, defined by ｜y′｜ 〉 ｜x′｜, and presenting phases λ（Ax ＋ By） with 0≤ A, B ≤ 1 and λ≥ 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A1 B and A involved. Our method extends to a more general family of phases. These results are relevant to problems of almost everywhere convergence of double Fourier and Walsh series.展开更多
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.
基金Supported by Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20090003110018)
文摘In this paper, the author studies the mapping properties for some general maximal op- erators and singular integrals on certain function spaces via Fourier transform estimates. Also, some concrete maximal operators and singular integrals are studied as applications.
基金the North China Electric Power University Youth Foundation(No.200611004)the Renmin University of China Science Research Foundation(No.30206104)
文摘The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.
基金supported by the National Natural Science Foundation of China(11726622)the Natural Science Foundation Projection of Chongqing,China(cstc2021jcyj-msxmX0705).
文摘We introduce a class of generalized Orlicz-type Auscher-Mourgoglou slice space,which is a special case of the Wiener amalgam.We prove versions of the Rubio de Francia extrapolation theorem in this space.As a consequence,we obtain the boundedness results for several classical operators,such as the Calderón-Zygmund operator,the Marcinkiewicz integrals,the Bochner-Riesz means and the Riesz potential,as well as variational inequalities for differential operators and singular integrals.As an application,we obtain global regularity estimates for solutions of non-divergence elliptic equations on generalized Orlicz-type slice spaces if the coefficient matrix is symmetric,uniformly elliptic and has a small(δ,R)-BMO norm for some positive numbers δ and R.
文摘We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type （1, 1） inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension.
基金Foundation item:the Education Commission of Shandong Province(J98P51)
文摘The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.
文摘We prove the boundedness from Lp（T2） to itself, 1 〈 p 〈∞, of highly oscillatory singular integrals Sf（x, y） presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of integration, roughly speaking, defined by ｜y′｜ 〉 ｜x′｜, and presenting phases λ（Ax ＋ By） with 0≤ A, B ≤ 1 and λ≥ 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A1 B and A involved. Our method extends to a more general family of phases. These results are relevant to problems of almost everywhere convergence of double Fourier and Walsh series.
