共查询到20条相似文献,搜索用时 640 毫秒
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《数学进展》2017,(3)
令L=-△+V是薛定谔算子,其中△是R~n上的拉普拉斯算子,并且非负位势V属于逆H?lder类Bq(q≥n/2).与算子L相关的Riesz变换记为T_1=V(-△+V)~(-1)和T_2=V~(-1/2)(-△+V)~(-1/2),对偶Riesz变换记为T_1~*=(-△+V)~(-1)V和T_2~*=(-△+V)~(-1/2)V~(-1/2).本文建立了T_1~*和T_2~*以及他们的交换子在与位势V∈Bq,q≥n/2相关的加权Morrey空间L_(α,V,ω)~(p,λ)(R~n)上的有界性.这些结果实质性地推广了一些已知的结果.作为应用,本文的结果可以应用于Hermite算子的情形. 相似文献
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任锋 《数学的实践与认识》2019,(18)
研究薛定谔型算子V~(β_1)▽(-△+V)~(-β_2).当位势函数V属于逆Holder函数类RH_s(sn/2)时,利用函数分解技巧,得到了这个算子在广义Morrey空间上的有界性质.这个结果丰富和改进了一些已有的一些结论. 相似文献
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《数学物理学报(A辑)》2016,(1)
研究了当b∈BMO时,与Schrdinger算子L=-△+V相关的Riesz位势算子的交换子[b,I_α~L]在Campanato型空间上的有界性,其中△是Laplace算子,V≠0是满足反向H(o|¨)lder不等式的非负函数. 相似文献
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《数学的实践与认识》2020,(4)
假设薛定谔算子L=-Δ+V中的非负位势函数V属于逆H(o|")lder函数类RH_s(s> n/2).本文我们证明了Riesz算子T_α=L~(-α)V~α(0 <α相似文献
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设L=-△_(H~n)+V是Heisenberg群H~n上的Schr(o|¨)dinger算子,其中△_(H~n)为H~n上的次Laplacian,V≠0为满足逆H(o|¨)lder不等式的非负函数.本文研究H~n上Riesz位势I_α~L=L~(-α/2)在Campanato型空间A_L~β和Hardy型空间H_L~p上的某些性质. 相似文献
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令L=-△+V是一个Schr(o)dinger算子,V是一个满足逆H(o)lder不等式的非负位势.在本文中,首先引入由分数阶热半群{e-tLα)t>0生成的Lusin面积函数,其次通过从属性公式和半群的正则性,我们用平方函数刻画与L相关的Hardy空间HnL/(n+γ)(Rn). 相似文献
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本文讨论了如下一类非线性薛定谔方程:-△u+V(x)u=f(u),x∈R^N,在H^1(R^N)中无穷多解的存在性,其中N≥3,V(x)是RN上的实值连续函数并且满足对(A)x∈R^N,V(z)≥V0>0. 相似文献
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Ferit G"{U}RB"{U}Z 《数学年刊B辑(英文版)》2020,41(1):77-98
Let L =-?+V(x) be a Schr?dinger operator, where ? is the Laplacian on ■~n,while nonnegative potential V(x) belonging to the reverse H?lder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schr?dinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schr?dinger 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. 相似文献
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Eigenvalues and Eigenfunctions of a Schr\"{o}dinger Operator Associated with a Finite
Combination of Dirac-Delta Functions and CH Peakons
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In this paper, we first study the Schr\"{o}dinger operators with the following weighted function $\sum\limits_{i=1}^n p_i \delta(x - a_i)$, which is actually a finite linear combination of Dirac-Delta functions, and then discuss the same operator equipped with the same kind of potential function. With the aid of the boundary conditions, all possible eigenvalues and eigenfunctions of the self-adjoint Schr\"{o}dinger operator are investigated. Furthermore, as a practical application, the spectrum distribution of such a Dirac-Delta type Schr\"{o}dinger operator either weighted or potential is well applied to the remarkable integrable Camassa-Holm (CH) equation. 相似文献
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Generalized local Morrey spaces and multilinear commutators generated by Marcinkiewicz integrals with rough kernel associated with Schr\"{o}dinger operators and local Campanato functions
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Ferit Gürbüz 《Journal of Applied Analysis & Computation》2018,8(5):1369-1384
Let $L=-\Delta+V\left( x\right) $ be a Schr\"{o}dinger operator, where $\Delta$ is the Laplacian on ${\mathbb{R}^{n}}$, while nonnegative potential $V\left( x\right) $ belongs to the reverse H\"{o}lder class. In this paper, we consider the behavior of multilinear commutators of Marcinkiewicz integrals with rough kernel associated with Schr\"{o}dinger operators on generalized local Morrey spaces. 相似文献
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刘建忠 《数学物理学报(A辑)》2012,32(1):171-185
利用H\"{o}lder不等式和β-函数, 得到了Hardy-Littlewood不等式的一些推广和改进形式. 作为应用, 通过所得结果及矩阵方法, 给出了Hilbert型不等式的一些推广和改进. 相似文献
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In this paper,we consider the strong dissipative KDV type equation on an unbounded domain R1.By applying the theory of decomposing operator and the method of constructing some compact operator in weighted space,the existence of exponential attractor in phase space H2(R1) is obtained. 相似文献
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本文讨论了在实轴上具有紧支集的势的薛定谔算子的极点散射问题. 本文旨在将狄利克雷级数理论与散射理论相结合, 文中运用了Littlewood的经典方法得到关于极点个数的新的估计. 本文首次将狄利克雷级数方法用于极点估计, 由此得到了极点个数的上界与下界, 这些结果改进和推广了该论题的一些相关结论. 相似文献
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In this paper, we consider the Schrödinger type operator ${H = (-\Delta _{\mathbb {H}}^n)^2 +V ^{2}}In this paper, we consider the Schr?dinger type operator
H = (-D\mathbb Hn)2 +V 2{H = (-\Delta _{\mathbb {H}}^n)^2 +V ^{2}}, where the nonnegative potential V belongs to the reverse H?lder class
Bq1 for q1 3 \frac Q 2,Q 3 6{B_{{q}_{1}}\, {\rm for}\, q_{1}\geq {\frac {Q}{ 2}},Q \geq 6}, and
D\mathbb Hn{\Delta_{\mathbb {H}^n}} is the sublaplacian on the Heisenberg group
\mathbb Hn{\mathbb {H}^n}. An L
p
estimate and a weak type L
1 estimate for the operator
?4\mathbb Hn H-1{\nabla^4_{\mathbb {H}^n} H^{-1}} when V ? Bq1{V \in B_{{q}_{1}}} for
1 < p £ \fracq12{1 < p \leq \frac{q_{1}}{2}} are obtained. 相似文献
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In this paper, we establish the existence and concentration of solutions of a class of nonlinear Schr?dinger equation $$- \varepsilon ^2 \Delta u_\varepsilon + V\left( x \right)u_\varepsilon = K\left( x \right)\left| {u_\varepsilon } \right|^{p - 2} u_\varepsilon e^{\alpha _0 \left| {u_\varepsilon } \right|^\gamma } , u_\varepsilon > 0, u_\varepsilon \in H^1 \left( {\mathbb{R}^2 } \right),$$ where 2 < p < ∞, α 0 > 0, 0 < γ < 2. When the potential function V (x) decays at infinity like (1 + |x|)?α with 0 < α ≤ 2 and K(x) > 0 are permitted to be unbounded under some necessary restrictions, we will show that a positive H 1(?2)-solution u ? exists if it is assumed that the corresponding ground energy function G(ξ) of nonlinear Schr?dinger equation $- \Delta u + V\left( \xi \right)u = K\left( \xi \right)\left| u \right|^{p - 2} ue^{\alpha _0 \left| u \right|^\gamma }$ has local minimum points. Furthermore, the concentration property of u ? is also established as ? tends to zero. 相似文献