The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) i...The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.展开更多
In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） an...In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.展开更多
Our aim in this paper is to prove the boundedness of commutators of Calderón-Zygmund operator with the Lipschitz function or BOM function on Herz-type Hardy space with variable exponent.
Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition a...We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.展开更多
In this paper,the authors introduce certain Herz type Hardy spaces with variable exponents and establish the characterizations of these spaces in terms of atomic and molecular decompositions. Using these decomposition...In this paper,the authors introduce certain Herz type Hardy spaces with variable exponents and establish the characterizations of these spaces in terms of atomic and molecular decompositions. Using these decompositions,the authors obtain the boundedness of some singular integral operators on the Herz type Hardy spaces with variable exponents.展开更多
The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
In this paper, we will obtain that the boundedness of multilinear n-dimensional fractional Hardy operators of variable order β(x) on variable exponent Herz-Morrey spaces.
Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positiv...Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).展开更多
For a century, hypothesis of a variable time is laid down by the Relativity Theory. This hypothesis can explain many Nature observations, experiments and formulas, for example the Lorentz factor demonstration. Because...For a century, hypothesis of a variable time is laid down by the Relativity Theory. This hypothesis can explain many Nature observations, experiments and formulas, for example the Lorentz factor demonstration. Because of such good explanations, the hypothesis of a variable time has been validated. Nevertheless, it remains some paradoxes and some predictions which are difficult to measure, as a reversible time or the time variation itself. The purpose of this article is to study another hypothesis. If it gives interesting results, it would mean that this alternative hypothesis can also be validated. The idea in this paper is to replace the variable time by a variable inertial mass. To the difference with the Theory of Relativity (where the inertial mass and the gravitational mass are equal and variable), the gravitational mass is here supposed to be constant. So, starting from the definition of the kinetic energy, it is introduced the Lorentz factor. And then it is demonstrated the value of the Lorentz factor thanks to a variable inertial mass. This variable inertial mass can also explain experiments, like Bertozzi experiment. If this alternative demonstration was validated, it could help to open doors, other physical effects could be explained like the addition of velocities.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
基金Supported by the973Project( G1 9990 75 1 0 5 ) and the National Natural Science Foundation of China( 1 0 2 71 0 1 6)
文摘The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.
基金supported by NSFC (No. 11201003)Education Committee of Anhui Province (No. KJ2012A133)
文摘In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.
文摘Our aim in this paper is to prove the boundedness of commutators of Calderón-Zygmund operator with the Lipschitz function or BOM function on Herz-type Hardy space with variable exponent.
基金Supported by the National Natural Science Foundation of China(1057115610871173)
文摘Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
文摘We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.
基金partially supported by the NSF of China (Grants No.11361020)the Natural Science Foundation of Hainan Province (No.20151011)
文摘In this paper,the authors introduce certain Herz type Hardy spaces with variable exponents and establish the characterizations of these spaces in terms of atomic and molecular decompositions. Using these decompositions,the authors obtain the boundedness of some singular integral operators on the Herz type Hardy spaces with variable exponents.
基金Supported by Zhejiang Provincial Natural Science Foundation of China under Grant (No.M103069)supported by the Education Dept. of Zhejiang Province(20021022)
文摘The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
基金Supported by the National Natural Science Foundation of China(11201003)Supported by the Education Committee of Anhui Province(KJ2012A133)
文摘In this paper, we will obtain that the boundedness of multilinear n-dimensional fractional Hardy operators of variable order β(x) on variable exponent Herz-Morrey spaces.
基金supported by the National Natural Science Foundation of China(11801555 and 11971058)the Fundamental Research Funds for the Central Universities(2020YQLX02)supported by the National Natural Science Foundation of China(11971058,11761131002 and 11671185)。
文摘Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).
文摘For a century, hypothesis of a variable time is laid down by the Relativity Theory. This hypothesis can explain many Nature observations, experiments and formulas, for example the Lorentz factor demonstration. Because of such good explanations, the hypothesis of a variable time has been validated. Nevertheless, it remains some paradoxes and some predictions which are difficult to measure, as a reversible time or the time variation itself. The purpose of this article is to study another hypothesis. If it gives interesting results, it would mean that this alternative hypothesis can also be validated. The idea in this paper is to replace the variable time by a variable inertial mass. To the difference with the Theory of Relativity (where the inertial mass and the gravitational mass are equal and variable), the gravitational mass is here supposed to be constant. So, starting from the definition of the kinetic energy, it is introduced the Lorentz factor. And then it is demonstrated the value of the Lorentz factor thanks to a variable inertial mass. This variable inertial mass can also explain experiments, like Bertozzi experiment. If this alternative demonstration was validated, it could help to open doors, other physical effects could be explained like the addition of velocities.
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="" />.
