共查询到20条相似文献,搜索用时 31 毫秒
1.
江寅生 《数学物理学报(B辑英文版)》2011,31(3):993-1000
Let ∠= -△H~n+ V be the Schrdinger operator on the Heisenberg groups H~n,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates of the fractional integrals associated to ∠. 相似文献
2.
Let L =-△ + V be the Schr dinger operator on Rd, where △ is the Laplacian on Rdand V≠0 is a nonnegative function satisfying the reverse H lder's inequality.The authors prove that Riesz potential Iβand its commutator [b, Iβ] associated with L map from Mp,qα,vinto Mp1,q1α,v. 相似文献
3.
Let L=△Hn + V be a Schrdinger operator on Heisenberg group H n,where △Hn is the sublaplacian and the nonnegative potential V belongs to the reverse H¨older class BQ/2,where Q is the homogeneous dimension of H n.Let T1 =(△Hn + V)-1 V,T2 =(△Hn +V)-1/2 V 1/2,and T 3 =(△Hn +V)-1/2 Hn,then we verify that [b,Ti],i = 1,2,3 are bounded on some Lp(Hn),where b ∈ BMO(Hn).Note that the kernel of Ti,i=1,2,3 has no smoothness. 相似文献
4.
JIANG Yin-sheng 《高校应用数学学报(英文版)》2012,27(1)
Let (L) =-△ + V be the Schr(o)dinger operator on Rd,d ≥ 3,where △ is the Laplacian on Rd and V (≠) 0 is a nonnegative function satisfying the reverse H(O)lder inequality.In this article,the author inve... 相似文献
5.
We introduce the BMO-type space bmoρ(ω) and establish the duality between h_ρ~1(ω) and bmo _ρ(ω),where ω∈A_1~(ρ, ∞)(R~n) and ω's locally behave as Muckenhoupt's weights but actually include them. We also give the Fefferman-Stein type decomposition of bmoρ(ω) with respect to Riesz transforms associated to Schrdinger operator L, where L =-? + V is a Schrdinger operator on R~n(n≥3) and V is a non-negative function satisfying the reverse Hlder inequality. 相似文献
6.
Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G. 相似文献
7.
Let A:=-(▽-ia(向量))·(?-ia(向量))+V be a magnetic Schrdinger operator on L~2(R~n),n≥2,where a(向量)=(a_1,···,a_n)∈L~2_(loc)(R~n,R~n) and 0≤V∈L~1_(loc)(R~n).In this paper,we show that for a function b in Lipschitz space Lip_α(R~n) with α∈(0,1),the commutator[b,V~(1/2)A~(-1/2)] is bounded from L_p(R~n) to L_q(R~n),where p,q∈(1,2] and 1/p-1/q =α/n. 相似文献
8.
Let L be a Schrdinger operator of the form L =-? + V acting on L~2(R~n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R~n) denote the BMO space associated to the Schrdinger operator L on R~n. In this article, we show that for every f ∈ BMO_L(R~n) with compact support, then there exist g ∈ L~∞(R~n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R~n), where S_(μ,P)=∫(R_+~(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-~(t(L)~(1/2))}t0 on L~2(R~n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R~n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators. 相似文献
9.
Let L =-? + V be a Schrdinger operator acting on L2(Rn), n ≥ 1, where V ≡ 0 is a nonnegative locally integrable function on Rn. In this article, we will intropduce weighted Hardy spaces H L(w) associated with L by means of the square function and then study their atomic decomposition theory. We will also show that the Riesz transform ?L-1/2associated with L is bounded from our new space Hp L(w) to the classical weighted Hardy space Hp(w) when n/(n +1) p 1 and w ∈ A1∩ RH(2/p)′. 相似文献
10.
Let L =-△Hn +V be a Schr(o)dinger operator on Heisenberg group Hn,where △Hn is the sublaplacian and the nonnegative potential V belongs to the reverse H(o)lder class BQ/2,where Q is the homogeneous dim... 相似文献
11.
Let L = L0+V be the higher order Schrdiger type operator where L0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coefficients and V is a real measurable function as multiplication operator(e.g., including(-?)m+V(m∈N) as special examples). In this paper, assume that V satisfies a strongly subcritical form condition associated with L0, the authors attempt to establish a theory of Hardy space Hp L(Rn)(0 p ≤ 1) associated with the higher order Schrdinger type operator L. Specifically, we first define the molecular Hardy space Hp L(Rn) by the so-called( p, q, ε, M) molecule associated to L and then establish its characterizations by the area integral defined by the heat semigroup e-t L. 相似文献
12.
Donggao Deng Yanbo Xu Lixin Yan 《分析论及其应用》2006,22(1):41-55
Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on Lp (X), 1 < p <∞. We give a sufficient condition on the kernel k(x,y) of Tso that when a function b ∈ BMO (X) ,the commutator [b, T] (f) = T (b f) - bT (f) is aounded on spaces Lp for all p, 1 < p <∞. 相似文献
13.
《分析论及其应用》2004,(3)
Schrdinger operator is a central subject in the mathematical study of quanturn mechanics.Consider the Schrodinger operator H=-△+Ⅴ on R,where △=d2/dx2 and the potentialfunction Ⅴ is real valued.In Fourier analysis.it is well—known that a square integrable functionadmits an expansion with exponentials as eigenfunctions of—△.A natural Conjecture is that anL2 function admits a similar expansion in terms of“eigenfunctions”of H,a perturbation of theLaplacian(see [7],Ch.Ⅺ and the notes),under certain condition on Ⅴ. 相似文献
14.
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
15.
《数学物理学报(B辑英文版)》2020,(1)
Let T be an anisotropic Calderón-Zygmund operator and φ:R~n×[0,∞)→[0,∞) be an anisotropic Musielak-Orlicz function with φ(x,·) being an Orlicz function andφ(·,t) being a Muckenhoupt A_∞(A) weight.In this paper,our goal is to study two boundedness theorems for commutators of anisotropic Calderon-Zygmund operators.Precisely,when b∈BMO_w(R~n,A)(a proper subspace of anisotropic bounded mean oscillation space BMO(R~n,A)),the commutator [b,T] is bounded from anisotropic weighted Hardy space H_ω~1(R~n,A) to weighted Lebesgue space L_ω~1(R~n) and when b∈BMO(R~n)(bounded mean oscillation space),the commutator [b,T] is bounded on Musielak-Orlicz space L~φ(R~n),which are extensions of the isotropic setting. 相似文献
16.
Let L be a Schr?dinger operator of the form L =-Δ + V acting on L~2(R~n) where the nonnegative potential V belongs to the reverse H?lder class B_q for some q ≥ n. In this article we will show that a function f ∈ L~(2,λ)(R~n), 0 λ n, is the trace of the solution of L_u =-u_(tt) + L_u =0, u(x, 0) = f(x), where u satisfies a Carleson type condition sup x_B,r_Br_B~(-λ)∫_0~(rB)∫_(B(x_B,r_B))t|u(x,t)|~2dxdt≤C∞.Its proof heavily relies on investigate the intrinsic relationship between the classical Morrey spaces and the new Campanato spaces L_L~(2,λ)(R~n) associated to the operator L, i.e.L_L~(2,λ)(R~n)=L~(2,λ)(R~n).Conversely, this Carleson type condition characterizes all the L-harmonic functions whose traces belong to the space L~(2,λ)(R~n) for all 0 λ n. 相似文献
17.
Shijun Zheng 《分析论及其应用》2009,25(1):79-85
We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schrdinger operator with electro-magnetic potential. 相似文献
18.
Wen-ming Li Shan-zhen Lu Hui-xia Mo 《应用数学学报(英文版)》2007,23(1):113-122
Let[b,T]be the commutator generated by a Lipschitz function b ∈ Lip(β)(0<β<1)and multiplierT.The authors studied the boundedness of[b,T]on the Lebesgue spaces and Hardy spaces. 相似文献
19.
Boundedness of higher order commutators of generalized fractional integral operators on Hardy spaces
Chunlei He Lisheng Shu 《分析论及其应用》2005,21(3):249-257
Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces. 相似文献
20.
Boundedness of commutators on Hardy type spaces 总被引:18,自引:0,他引:18
Let [b, T] be the commutator of the function b ∈ Lipβ(Rn) (0 <β≤ 1) and the CalderónZygmund singular integral operator T. The authors study the boundedness properties of [b, T] on the classical Hardy spaces and the Herz-type Hardy spaces in non-extreme cases. For the boundedness of these commutators in extreme cases, some characterizations are also given. Moreover, the authors prove that these commutators are bounded from Hardy type spaces to the weak Lebesgue or Herz spaces in extreme cases. 相似文献