共查询到20条相似文献,搜索用时 81 毫秒
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假设n和m是两个正整数,P(x,D)是定义在维数为n的紧致无边流形M上的一般m阶椭圆自伴微分算子.在一定条件下,本文主要证明微分算子P(x,D)的预解式的一致L^p-L^q估计,其中n〉m≥2,(p,q)在Sobolev线上并满足1/p-1/q=m/n,p≤2(n+1)/n+3,q≥2(n+1)/n-1.本文的一个核心引理是建立曲面Σx={ξ∈Tx^*(M):p(x,ξ)=1}上测度的Fourier变换衰减估计的具体表达式,并利用它来得到局部算子的一致L^p-L^q估计. 相似文献
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本文将给出Heisenberg型群上的一些强奇异卷积算子的L^2有界性.特别地,本文的结果改进并推广了Laghi和Lyall在Heisenberg群上的相应工作.此外,一些更简单、有效的技巧也在本文中引入. 相似文献
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本文考虑Euclid空间Rn中环B1/B∈上的调和函数u,其中∈〈〈1.本文证明当1〈p〈∞时,在合适的边界条件下,▽u的Lp,1(B1/2/B2∈)范数可以被▽u的L^p,∞(B1/B∈)范数控制,其中的常数不依赖于∈. 相似文献
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本文介绍一类带有非对称正核的完全非线性混合可积微分算子并研究其解的正则性.具体地,本文建立关于该算子非局部A-B-P(Alexandroff-Bakelman-Pucci)估计、Harnack不等式以及解的Holder和C1,α正则性. 相似文献
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本文考虑多线性Fourier乘子算子在加权Lebesgue空间的乘积空间上的性质,利用多线性Fourier乘子算子的核估计以及多线性奇异积分算子的加权理论,建立多线性Fourier乘子算子的(关于多重Ap/r(R^mn)权函数以及关于一般权函数的)两个加权估计. 相似文献
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《数学学报》2013,(5)
考虑了一致抛物型算子■=_t-∑_(i,j)n=_1_i(a_(i,j)(x)_j)+V(x),其中势函数V(x)是Rn=_1_i(a_(i,j)(x)_j)+V(x),其中势函数V(x)是Rn(n≥3)上的非负函数,并且属于反霍尔德类.得到了算子(?)的基本解的梯度估计,以及算子V■n(n≥3)上的非负函数,并且属于反霍尔德类.得到了算子(?)的基本解的梯度估计,以及算子V■(-1),V(-1),V(1/2)▽■(1/2)▽■(-1)和V(-1)和V(1/2)(1/2)(-1/2)在加权L(-1/2)在加权Lp(Rp(R(n+1))空间和Morrey空间上的估计. 相似文献
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In this work we obtain boundedness on suitable weighted BMO type spaces of Riesz transforms, and their adjoints, associated to the Schrödinger operator −Δ+V, where V satisfies a reverse Hölder inequality. Our results are new even in the unweighted case. 相似文献
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S Molchanov 《Journal of Functional Analysis》2004,215(1):111-129
It is proven that the absolutely continuous spectrum of matrix Schrödinger operators coincides (with the multiplicity taken into account) with the spectrum of the unperturbed operator if the (matrix) potential is square integrable. The same result is also proven for some classes of slower decaying potentials if they are smooth. 相似文献
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Let L = ?Δ + V be a Schrödinger operator on $\mathbb {R}^nLet L = ?Δ + V be a Schrödinger operator on $\mathbb {R}^n$ (n ≥ 3), where $V \not\equiv 0$ is a nonnegative potential belonging to certain reverse Hölder class Bs for $s \ge \frac{n}{2}$. In this article, we prove the boundedness of some integral operators related to L, such as L?1?2, L?1V and L?1( ? Δ) on the space $BMO_L(\mathbb {R}^n)$. 相似文献
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In this paper we obtain local L
p
estimates for the parabolic polyharmonic equations by a straightforward approach.
Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic
Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported
by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant
No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017) 相似文献
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Zhongwei Shen 《Transactions of the American Mathematical Society》1996,348(11):4465-4488
We consider the Schrödinger operator with magnetic field,
Assuming that and is locally in certain reverse Hölder class, we study the eigenvalue asymptotics and exponential decay of eigenfunctions.
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Marcelo F. Furtado 《Journal of Mathematical Analysis and Applications》2005,304(1):170-188
We deal with the quasilinear Schrödinger equation
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For the spectral expansions related to the Schrödinger operator with constant magnetic field we establish Riesz-Bochner summability in Lp. 相似文献
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S. Albeverio S. Kuzhel S. Torba 《Journal of Mathematical Analysis and Applications》2008,338(2):1267-1281
A p-adic Schrödinger-type operator Dα+VY is studied. Dα (α>0) is the operator of fractional differentiation and (bij∈C) is a singular potential containing the Dirac delta functions δx concentrated on a set of points Y={x1,…,xn} of the field of p-adic numbers Qp. It is shown that such a problem is well posed for α>1/2 and the singular perturbation VY is form-bounded for α>1. In the latter case, the spectral analysis of η-self-adjoint operator realizations of Dα+VY in L2(Qp) is carried out. 相似文献
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In this paper we consider the SchrSdinger operator -△G + W on the nilpotent Lie group G where the nonnegative potential W belongs to the reverse H51der class Bq1 for some q1 ≥ D and D is the dimension at infinity of G. The weighted L^p -L6q estimates for the operators W^a(-△G + W)^-β and W^a△G(-△G + W)^-β are obtained. 相似文献
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In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions. 相似文献