共查询到20条相似文献,搜索用时 140 毫秒
1.
On commutators of fractional integrals 总被引:1,自引:0,他引:1
Xuan Thinh Duong Li Xin Yan 《Proceedings of the American Mathematical Society》2004,132(12):3549-3557
Let be the infinitesimal generator of an analytic semigroup on with Gaussian kernel bounds, and let be the fractional integrals of for . For a BMO function on , we show boundedness of the commutators from to , where . Our result of this boundedness still holds when is replaced by a Lipschitz domain of with infinite measure. We give applications to large classes of differential operators such as the magnetic Schrödinger operators and second-order elliptic operators of divergence form.
2.
A. M. Sedletskii 《Analysis Mathematica》2002,28(1):43-60
D Ranee avtorom byli postroeny sistemy vida $$e^{-i lambda_n t} \exp (-a|t|^\alpha), \quad \lambda_n \in \Lambda; \quad a>0, \ \alpha>1,\leqno(1)$$ polnye i minimal\cprime nye v prostranstvakh $L^p ({\bf R})$ $(L^p ({\bf R}_+))$ pri $p\ge 2$. V danno\u i\ stat\cprime e stroyat\cydot sya sistemy (1), obladayushchie takim svo\u istvom v prostranstvakh $L^p({\bf R})$ $(L^p ({\bf R}_+))$, $1\le p <2$ i $C_0 ({\bf R})$ $(C_0 ({\bf R}_+))$. 相似文献
3.
该文讨论了如下具有退化粘性的非齐次双曲守恒律方程的Cauchy问题$\left\{\begin{array}{l} u_t+f(u)_x=a^2t^\alpha u_{xx}+g(u),\ \ \ x\in{\bf R},\ \ \ t>0,\\u(x,0)=u_0(x) \in L^\infty({\bf R}).\end{array}\right.\eqno{({\rm I})}$其中$f(u), g(u)$是${\bf R}$上的光滑函数, $a>0, 0<\alpha<1$均为常数.在此条件下, 作者首先给出了Cauchy问题(I)的局部解的存在性, 再利用极值原理获得了解的$L^{\infty}$估计, 从而证明了Cauchy问题(I)整体光滑解的存在性. 相似文献
4.
We study the large time behavior of the solutions of the Cauchy problem for a semilinear heat equation,
$\partial_t u=\Delta u+F(x,t,u) \quad{\rm in}
\;{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad{\rm in}
\;{\bf R}^N,\quad\quad ({\rm P})$\partial_t u=\Delta u+F(x,t,u) \quad{\rm in}
\;{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad{\rm in}
\;{\bf R}^N,\quad\quad ({\rm P}) 相似文献
5.
In this paper,the boundedness for the multilinear commutators of Bochner-Riesz operator is considered.We prove that the multilinear commutators generated by Bochner-Riesz operator and Lipschitz function are bounded from Lp(Rn)into ∧˙(β-np)(Rn)and from Lnβ(Rn)into BMO(Rn). 相似文献
6.
对x=(x_1,…,x_n)∈[0,1)~n∪(1,+∞o)~n,定义对称函数■其中r∈N,i_1,i_2,…,i_n为非负整数.研究了F_n(x,r)的Schur凸性、Schur乘性凸性和Schur调和凸性.作为应用,用控制理论建立了一些不等式,特别地,给出了高维空间的一些新的几何不等式. 相似文献
7.
We study large time asymptotics of solutions to the BBM–Burgers equation
8.
Jonathan Bennett 《Proceedings of the American Mathematical Society》1999,127(3):715-723
A generalised integral is used to obtain a Fourier multiplier relation for Calderón-Zygmund operators on . In particular we conclude that an operator in our class is injective on if it is injective on .
9.
Curtis T. McMullen 《Journal of the American Mathematical Society》2005,18(3):711-734
Let be the diagonal subgroup, and identify with the space of unimodular lattices in . In this paper we show that the closure of any bounded orbit
meets the set of well-rounded lattices. This assertion implies Minkowski's conjecture for and yields bounds for the density of algebraic integers in totally real sextic fields. The proof is based on the theory of topological dimension, as reflected in the combinatorics of open covers of and . 10.
In this paper, the authors give the local L~2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equations(~*) along a curve γ:■where φ : R~+→R satisfies some suitable conditions and φ((-?)~(1/2)) is a pseudo-differential operator with symbol φ(|ξ|). As a consequence of the above result, the authors give the pointwise convergence of the solution(when n = 1) of the equation(~*) along curve γ.Moreover, a global L~2 estimate of the maximal operator S_(φ,γ)~* is also given in this paper. 相似文献
11.
Jiang Jifa 《数学年刊B辑(英文版)》1996,17(3):335-342
51.IntroductionBeginingwiththepath-breakingworkofM.W.HirschI1-4]forcooperativesystemsandmonotonesemiflows,thereisnowanextensiveliteratureoncooperativesystemsandmoncatonedynamicalsystems.Assumingthatthesystemiscooperativeandirreducible,HirschshowedthataImosteveryforwardorbitwithcompactclosure,inthesenseofLebesguemeasure,tendstoequilibriaast- oc(see2,Theorem4.l]).Asimilarresultholdsforastronglymonotonesemifiowonastronglyorderspace(see[4,Theoremo.1]).Manypeoplehavegivensomeadditionalconditio… 相似文献
12.
Yun-Zhang Li 《Proceedings of the American Mathematical Society》2005,133(8):2419-2428
The study of Gabor bases of the form for has interested many mathematicians in recent years. Alex Losevich and Steen Pedersen in 1998, Jeffery C. Lagarias, James A. Reeds and Yang Wang in 2000 independently proved that, for any fixed positive integer , is an orthonormal basis for if and only if is a tiling of . Palle E. T. Jorgensen and Steen Pedersen in 1999 gave an explicit characterization of such for , , . Inspired by their work, this paper addresses Gabor orthonormal bases of the form for and some other related problems, where is as above. For a fixed , the generating function of a Gabor orthonormal basis for corresponding to the above is characterized explicitly provided that , which is new even if ; a Shannon type sampling theorem about such is derived when , ; for an arbitrary positive integer , an explicit expression of the with being an orthonormal basis for is obtained under the condition that .
13.
The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order $H^m(\mathbb {H}^n), m\in \mathbb {N}^n,$ under the heat kernel transform on $\mathbb {H}^n,$ using direct sum and direct integral of Bergmann spaces and certain unitary representations of $\mathbb {H}^n$ which can be realized on the Hilbert space of Hilbert‐Schmidt operators on $L^2(\mathbb {R}^n).$ We also show that the image of Sobolev space of negative order $H^{-s}(\mathbb {H}^n), s(>0) \in \mathbb {R}$ is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on $\mathbb {H}^n$ under the heat kernel transform. 相似文献
14.
Denote by
the real-linear span of
, where
Under the concept of left-monogeneity defined through the generalized
Cauchy-Riemann operator we obtain the direct sum decomposition of
15.
L. A. Coburn 《Proceedings of the American Mathematical Society》2007,135(4):1163-1168
F.A. Berezin introduced a general ``symbol calculus" for linear operators on reproducing kernel Hilbert spaces. For the Segal-Bargmann space of Gaussian square-integrable entire functions on complex -space, , or for the Bergman spaces of Euclidean volume square-integrable holomorphic functions on bounded domains in , we show here that earlier Lipschitz estimates for Berezin symbols of arbitrary bounded operators are sharp.
16.
Weiyang Chen & Xiaoli Chen 《数学研究》2014,47(2):208-220
In this paper, we are concerned with the properties of positive solutions of the following nonlinear integral systems on the Heisenberg group $\mathbb{H}^n$, \begin{equation} \left\{\begin{array}{ll} u(x)=\int_{\mathbb{H}^n}\frac{v^{q}(y)w^{r}(y)}{|x^{-1}y|^\alpha|y|^\beta}\,dy,\\ v(x)=\int_{\mathbb{H}^n}\frac{u^{p}(y)w^{r}(y)}{|x^{-1}y|^\alpha|y|^\beta}\,dy,\\ w(x)=\int_{\mathbb{H}^n}\frac{u^{p}(y)v^{q}(y)}{|x^{-1}y|^\alpha|y|^\beta}\,dy,\\ \end{array}\right.\end{equation} for $x\in \mathbb{H}^n$, where $0<\alpha
1$ satisfying $\frac{1}{p+1} $+ $\frac{1}{q+1} + \frac{1}{r+1} = \frac{Q+α+β}{Q}.$ We show that positive solution triples $(u,v,w)\in L^{p+1}(\mathbb{H}^n)\times L^{q+1}(\mathbb{H}^n)\times L^{r+1}(\mathbb{H}^n)$ are bounded and they converge to zero when $|x|→∞.$ 相似文献 17.
18.
Thomas Kuhn Hans-Gerd Leopold Winfried Sickel Leszek Skrzypczak 《Constructive Approximation》2005,23(1):61-77
We investigate the asymptotic behavior of the entropy numbers of the
compact embedding
$$
B^{s_1}_{p_1,q_1} \!\!(\mbox{\footnotesize\bf R}^d, \alpha) \hookrightarrow B^{s_2}_{p_2,q_2} \!\!({\xxR}).
$$
Here $B^s_{p,q} \!({\mbox{\footnotesize\bf R}^d}, \alpha)$ denotes a weighted Besov space, where the weight is
given by $w_\alpha (x) = (1+| x |^2)^{\alpha/2}$, and
$B^{s_2}_{p_2,q_2} \!({\mbox{\footnotesize\bf R}^d})$ denotes the unweighted Besov space, respectively.
We shall concentrate
on the so-called limiting situation given by the following constellation of
parameters: $s_2 < s_1$, $0 < p_1,p_2 \le \infty$, and
$$
\alpha = s_1 - \frac{d}{p_1} - s_2 + \frac{d}{p_2} >
d \, \max \Big(0, \frac{1}{p_2}-\frac{1}{p_1}\Big).
$$
In almost all cases we give a sharp two-sided estimate. 相似文献
19.
Hui Yin Shuyue Chen Jing Jin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,1(2):969-1001
This paper is concerned with the large time behavior of traveling wave solutions to the Cauchy problem of generalized Benjamin–Bona–Mahony–Burgers
equations
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