Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almo...Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.展开更多
In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [<em>b</em>,<em>μ</em><sub>Ω</sub>] and obtain the result with ...In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [<em>b</em>,<em>μ</em><sub>Ω</sub>] and obtain the result with Lipschitz function and BMO function f on the Herz-Morrey-Hardy spaces with variable exponents <img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" width="0" height="0" alt="" /><img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" alt="" />.展开更多
The singular integral operator FΩ.a, and the Marcinkiewicz integral operator μ^-Ω.a are studied. The kernels of the operators behave like ｜y｜^-n-a（a〉0） near the origin, and contain an oscillating factor e^i｜y...The singular integral operator FΩ.a, and the Marcinkiewicz integral operator μ^-Ω.a are studied. The kernels of the operators behave like ｜y｜^-n-a（a〉0） near the origin, and contain an oscillating factor e^i｜y｜^-β（β〉0） and a distribution Ω on the unit sphere S^n-1. It is proved that, if Ω is in the Hardy space H^r（S^n-1） with 0〈r=（n-1）/（n-1＋y）（r〉0）, and satisfies certain eancellation condition,then FΩ.a and μ^-Ω.a extend the bounded operator from Sobolev space L^pr to Lebesgue space L^p for some p. The result improves and extends some known results.展开更多
Let L =-△+V(x) be a Schrodinger operator, where △ is the Laplacian on R^n,while nonnegative potential V(x) belonging to the reverse Holder class. The aim of this paper is to give generalized weighted Morrey estimate...Let L =-△+V(x) be a Schrodinger operator, where △ is the Laplacian on R^n,while nonnegative potential V(x) belonging to the reverse Holder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schrodinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.展开更多
Abstract In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain Rn ×RM （n, m ≥2） are introduced. Lp bounds of such operators are obtained under weak conditions on the ke...Abstract In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain Rn ×RM （n, m ≥2） are introduced. Lp bounds of such operators are obtained under weak conditions on the kernels.展开更多
The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. Lp estimates, as well as the corresponding weighted estimates of such maximal ...The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. Lp estimates, as well as the corresponding weighted estimates of such maximal functions, are obtained. Moreover, several applications of our results are highlighted.展开更多
文摘Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.
文摘In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [<em>b</em>,<em>μ</em><sub>Ω</sub>] and obtain the result with Lipschitz function and BMO function f on the Herz-Morrey-Hardy spaces with variable exponents <img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" width="0" height="0" alt="" /><img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" alt="" />.
文摘The singular integral operator FΩ.a, and the Marcinkiewicz integral operator μ^-Ω.a are studied. The kernels of the operators behave like ｜y｜^-n-a（a〉0） near the origin, and contain an oscillating factor e^i｜y｜^-β（β〉0） and a distribution Ω on the unit sphere S^n-1. It is proved that, if Ω is in the Hardy space H^r（S^n-1） with 0〈r=（n-1）/（n-1＋y）（r〉0）, and satisfies certain eancellation condition,then FΩ.a and μ^-Ω.a extend the bounded operator from Sobolev space L^pr to Lebesgue space L^p for some p. The result improves and extends some known results.
文摘Let L =-△+V(x) be a Schrodinger operator, where △ is the Laplacian on R^n,while nonnegative potential V(x) belonging to the reverse Holder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schrodinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.
文摘Abstract In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain Rn ×RM （n, m ≥2） are introduced. Lp bounds of such operators are obtained under weak conditions on the kernels.
文摘The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. Lp estimates, as well as the corresponding weighted estimates of such maximal functions, are obtained. Moreover, several applications of our results are highlighted.
