共查询到20条相似文献,搜索用时 15 毫秒
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We study Hardy and BMO spaces associated with the Grushin operator. We first prove atomic and maximal functions characterizations of the Hardy space. Further we establish a version of Fefferman–Stein decomposition of BMO functions associated with the Grushin operator and then obtain a Riesz transforms characterization of the Hardy space. 相似文献
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研究非线性算子方程的近似求解方法.首先对通常的求解非线性方程加速迭代格式进行推广,得到高阶收敛速度的加速迭代格式,最后把这种加速迭代格式推广到非线性算子方程的求解中去,利用非线性算子的渐进展开,证明了这种加速格式具有三阶的收敛速度. 相似文献
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We describe weighted restriction (Plancherel) type estimates and sharp Hebisch-Müller-Stein type spectral multiplier result for a new class of Grushin type operators. We also discuss the optimal exponent for Bochner-Riesz summability in this setting. 相似文献
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Nuri Murat Yagmurlu Yusuf Ucar Ihsan Celikkaya 《Journal of Applied Analysis & Computation》2018,8(5):1494-1510
In this study, the numerical behavior of the one-dimensional Regularized Long Wave (RLW) equation has been sought by the Strang splitting technique with respect to time. For this purpose, cubic B-spline functions are used with the finite element collocation method. Then, single solitary wave motion, the interaction of two solitary waves and undular bore problems have been studied and the effectiveness of the method has been investigated. The new results have been compared with those of some of the previous studies available in the literature. The stability analysis has also been taken into account by the von Neumann method. 相似文献
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Let Q be a bounded open domain in R^n with smooth boundaryаΩ.Let X=(X1,X2…,Xm)be a system of general Grushin type vector fields defined onΩand the boundaryаΩis non-characteristic for X.For△x=∑j=1^mXj^2,we denoteλk as the k-th eigenvalue for the bi-subelliptic operator△X2^2 onΩ.In this paper,by using the sharp sub-elliptic estimates and maximally hypoeliptic estimates,we give the optimal lower bound estimates ofλk for the operatork△X^2. 相似文献
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Let w(x), u(x) and (x) be weight functions. In this paper, underappropriate conditions on Young's functions 1, 2 we characterizethe inequality
for the Hardy-typeoperator T defined in [1] and the inequality
for the fractional maximal operator M, ; definedin [8], as well as the corresponding weak-type inequalities. 相似文献
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Miroslav Brzezina 《Mathematische Nachrichten》1994,169(1):59-67
For the Kolmogorov operator we describe all transformations mapping solutions of the equation Lu = 0 into solutions. 相似文献
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In this talk, we discuss the solvability of the operator equation SX-XT=Q, where S and -T are generators of some semigroups of operators. 相似文献
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《复变函数与椭圆型方程》2012,57(6):521-535
In this paper new solutions of the Bauer-Peschl equation represented by differential operators are derived. A relation to the solutions of Bauer is given. Furthermore, it will be said in which new way Bauer's solutions can be obtained. Also three other ways for obtaining the solutions of the Bauer-Peschl equation are sketched. 相似文献
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在一般的Banach空间中讨论了φ-强增生算子方程的琴点和φ-强伪压缩映象不动点的迭代逼近问题. 相似文献
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We show that Riesz transforms associated to the Grushin operator G = ?Δ ? |x|2~ t 2 are bounded on L p (? n+1). We also establish an analogue of the Hörmander-Mihlin Multiplier Theorem and study Bochner-Riesz means associated to the Grushin operator. The main tools used are Littlewood-Paley theory and an operator-valued Fourier multiplier theorem due to L. Weis. 相似文献
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一类多值算子方程的迭代算法 总被引:1,自引:0,他引:1
本讨论Hilbert空间上具有强单调、上半Lipschitz连续性质的多值算子方程的求解方法,构造了迭代格式并证明迭代过程是收敛的;同时给出它在求解多值微分方程边值问题中的应用。 相似文献
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证明了几个重要不等式,并研究了几类不同边界条件下随机半闭1-集压缩算子方程随机解的存在情况,得到了若干新的结果. 相似文献
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魏利 《应用泛函分析学报》2007,9(3):220-226
利用Calvert和Gupta关于非线性增生映射值域之和的扰动定理,得到了一类含有p拉普拉斯算子Δp的非线性Neumann边值问题在Lp(Ω)空间中解的存在性的结论,其中2N/(N 1)
相似文献
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Let x=(x',x')with x'∈Rk and x'∈R^N-k andΩbe a x'-symmetric and bounded domain in R^N(N≥2).We show that if 0≤a≤k-2,then there exists a positive constant C>0 such that for all x'-symmetric function u∈C0^∞(Ω)with∫Ω|■u(x)|^N-a|x'|^-adx≤1,the following uniform inequality holds1/∫Ω|x|^-adx∫Ωe^βa|u|N-a/N-a-1|x'|^-adx≤C,whereβa=(N-a)(2πN/2Γ(k-a/2)Γ(k/2)/Γ(k/2)r(N-a/2))1/N-a-1.Furthermore,βa can not be replaced by any greater number.As the application,we obtain some weighted Trudinger–Moser inequalities for x-symmetric function on Grushin space. 相似文献
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刘海蓉 《数学物理学报(B辑英文版)》2018,38(1):237-247
In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-harmonic basis. As an application of the orthogonal basis, the author proves a Liouville-type theorem for the Grushin operator, that is the Grushin-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant. 相似文献