共查询到20条相似文献,搜索用时 31 毫秒
1.
Operators related to truncated Hilbert transforms on <Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript>
下载免费PDF全文
![点击此处可从《数学学报(英文版)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Hong Hai Liu 《数学学报(英文版)》2017,33(7):1011-1020
In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H 1 to L 1, and prove variation, oscillation and λ-jump operators related to smooth truncations are bounded from H 1 to L 1. 相似文献
2.
Qing Guo 《应用数学学报(英文版)》2016,32(1):137-162
We investigate the nonlinear Schrödinger equation iu t +Δu+|u| p?1 u = 0with 1+ 4/N < p < 1+ 4/N?2 (when N = 1, 2, 1 + 4/N < p < ∞) in energy space H 1 and study the divergent property of infinite-variance and nonradial solutions. If \(M{\left( u \right)^{\frac{{1 - {s_C}}}{{{s_C}}}}}E\left( u \right) \prec M{\left( Q \right)^{\frac{{1 - {s_C}}}{{{s_C}}}}}E\left( Q \right)\) and \(\left\| {{u_0}} \right\|_2^{\frac{{1 - {s_c}}}{{{s_c}}}}\left\| {\nabla {u_0}} \right\|_2^{\frac{{1 - {s_c}}}{{{s_c}}}}{\left\| {\nabla Q} \right\|_2}\), then either u(t) blows up in finite forward time or u(t) exists globally for positive time and there exists a time sequence t n → +∞ such that \({\left\| {\nabla u\left( {{t_n}} \right)} \right\|_2} \to + \infty \). Here Q is the ground state solution of ?(1?s c )Q+ΔQ+Q p?1 Q = 0. A similar result holds for negative time. This extend the result of the 3D cubic Schrödinger equation obtained by Holmer to the general mass-supercritical and energy-subcritical case. 相似文献
3.
In this paper we use the real differential geometric definition of a metric (a unimodular oriented metric) tt*-bundle of Cortés and the author (Topological-anti-topological fusion equations, pluriharmonic maps and special Kähler manifolds) to define a map Φ from the space of metric (unimodular oriented metric) tt*-bundles of rank r over a complex manifold M to the space of pluriharmonic maps from M to {GL}(r)/O(p,q) (respectively {SL}(r)/SO(p,q)), where (p,q) is the signature of the metric. In the sequel the image of the map Φ is characterized. It follows, that in signature (r,0) the image of Φ is the whole space of pluriharmonic maps. This generalizes a result of Dubrovin (Comm. Math. Phys. 152 (1992; S539–S564). 相似文献
4.
DRAŽEN ADAMOVIĆ 《Transformation Groups》2016,21(2):299-327
We shall first present an explicit realization of the simple N = 4 superconformal vertex algebra L c N?=?4 with central charge c = ?9. This vertex superalgebra is realized inside of the bcβγ system and contains a subalgebra isomorphic to the simple affine vertex algebra L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \). Then we construct a functor from the category of L c N?=?4 -modules with c = ?9 to the category of modules for the admissible affine vertex algebra L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \). By using this construction we construct a family of weight and logarithmic modules for L c N?=?4 and L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \). We also show that a coset subalgebra L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \) is a logarithmic extension of the W(2; 3)-algebra with c = ?10. We discuss some generalizations of our construction based on the extension of affine vertex algebra L A1 (kΛ 0) such that k + 2 = 1/p and p is a positive integer. 相似文献
5.
It is well known that if m is an L p -multiplier for the Fourier transform on \({\mathbb{R}^n}\) , (1 < p < ∞) then there exists a pseudomeasure σ such that T m f = σ * f . A similar problem is discussed for the L p ?Fourier multipliers for \({\mathcal{H}}\) -valued functions on the Heisenberg group, where \({\mathcal{H}}\) is a separable Hilbert space. 相似文献
6.
Sungeun Jung 《中国科学 数学(英文版)》2018,61(5):881-896
Given a unilateral forward shift S acting on a complex, separable, innite dimensional Hilbert space H, an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that {S* n TS n } is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H. In this paper, we study the asymptotic T u -Toeplitzness of weighted composition operators on the Hardy space H2, where u is a nonconstant inner function. 相似文献
7.
V. S. Mokeichev 《Russian Mathematics (Iz VUZ)》2017,61(7):25-34
We present conditions that allow us to prove the existence of eigenvalues and characteristic values for operator F(D) ? C(λ): L 2(R m ) → L 2(R m ), where F(D) is a pseudo-differential operator with a symbol F(iξ) and C(λ): L 2(R m ) → L 2(R m ) is a linear continuous operator. 相似文献
8.
F. Galaz-Fontes 《Positivity》2010,14(4):715-729
For a vector measure ν having values in a real or complex Banach space and \({p \in}\) [1, ∞), we consider L p (ν) and \({L_{w}^{p}(\nu)}\), the corresponding spaces of p-integrable and scalarly p-integrable functions. Given μ, a Rybakov measure for ν, and taking q to be the conjugate exponent of p, we construct a μ-Köthe function space E q (μ) and show it is σ-order continuous when p > 1. In this case, for the associate spaces we prove that L p (ν) × = E q (μ) and \({E_q(\mu)^\times = L_w^p(\nu)}\). It follows that \({L_p (\nu) ^{**} = L_w^p (\nu)}\). We also show that L 1 (ν) × may be equal or not to E ∞ (μ). 相似文献
9.
M. G. Grigoryan 《Russian Mathematics (Iz VUZ)》2008,52(5):20-31
For any 0 < ? < 1 one can find a measurable set E ? [0, 1] with the measure |E| > 1 ? ? such that for each function f(x) ε L 1 (0, 1) a function g(x) ε L 1 (0, 1) exists such that it coincides with f (x) on E, its Fourier—Walsh series converges to it in the metric of L 1 (0, 1), and all nonzero terms of the sequence of Fourier coefficients of the new function obtained by the Walsh system have the modulo decreasing order; consequently, the greedy algorithm for this function converges to it in the L 1 (0, 1)-norm. 相似文献
10.
Let M Ω be the maximal operator with homogeneous kernel Ω. In the present paper, we show that if Ω satisfies the L 1-Dini condition on ?? n?1, then the following weak type (1,1) behaviors
hold for the maximal operator M Ω and \(f\in L^{1}(\mathbb {R}^{n})\), here \(\tilde {\omega }_{1}\) denotes the L 1 integral modulus of continuity of Ω defined by translation in \(\mathbb {R}^{n}\). 相似文献
$$\lim\limits _{\lambda \rightarrow 0_{+}}\lambda m(\{x\in \mathbb {R}^{n}:M_{\Omega } f(x)>\lambda \})=\frac {1}{n} \|\Omega \|_{1} \|f\|_{1},$$
$$\sup\limits_{\lambda >0}\lambda m(\{x\in \mathbb {R}^{n}:M_{\Omega } f(x)>\lambda \})\lesssim {\bigg ((\log n)\|\Omega \|_{1}+{\int }_{0}^{1/n}\frac {\tilde {\omega }_{1}(\delta )}{\delta }d\delta \bigg )}\|f\|_{1}$$
11.
F. Abtahi 《Acta Mathematica Hungarica》2011,133(4):324-331
Let G be a locally compact group, ω a weight function on G, and 1<p<∞. We introduce the Lebesgue weighted L p -space \({\mathcal{L}}_{\omega}^{1,p}(G)= L^{p}(G,\omega)\cap L^{1}(G)\) as a Banach space and introduce its dual. Furthermore, we consider this space as a Banach algebra with respect to the usual convolution and show that \({\mathcal{L}}_{\omega}^{1,p}(G)\) admits a bounded approximate identity if and only if G is discrete. In addition, we prove that amenability of this algebra implies that G is discrete and amenable. Moreover, we discuss the converse of this result. 相似文献
12.
Given an indexing set I and a finite field Kα for each α ∈ I, let ? = {L2(Kα) | α ∈ I} and \(\mathfrak{N} = \{ SL_2 (K_\alpha )|\alpha \in I\}\). We prove that each periodic group G saturated with groups in \(\Re (\mathfrak{N})\) is isomorphic to L2(P) (respectively SL2(P)) for a suitable locally finite field P. 相似文献
13.
Integral modular categories of Frobenius-Perron dimension pq n , where p and q are primes, are considered. It is already known that such categories are group-theoretical in the cases of 0 ≤ n ≤ 4. In the general case we determine that these categories are either group-theoretical or contain a Tannakian subcategory of dimension q i for i > 1. We then show that all integral modular categories \(\mathcal {C}\) with \(\text {FPdim}(\mathcal {C})=pq^{5}\) are group-theoretical, and, if in addition p < q, all with \(\text {FPdim}(\mathcal {C})=pq^{6}\) or pq 7 are group-theoretical. In the process we generalize an existing criterion for an integral modular category to be group-theoretical. 相似文献
14.
Huixue Lao 《Acta Appl Math》2010,110(3):1127-1136
Let L(sym j f,s) be the jth symmetric power L-function attached to a holomorphic Hecke eigencuspform f(z) for the full modular group, and \(\lambda_{\mathrm{sym}^{j}f}(n)\) denote its nth coefficient. In this paper we are able to prove that and
相似文献
$\int_{1}^{x}\bigg|\sum_{n\leq y}\lambda_{\mathrm{sym}^{3}f}(n)\bigg|^{2}dy=O\bigl(x^{2}\bigr),$
$\int_{1}^{x}\bigg|\sum_{n\leq y}\lambda_{\mathrm{sym}^{4}f}(n)\bigg|^{2}dy=O\bigl(x^{\frac{11}{5}}\log x\bigr).$
15.
For a new class of g(t, x), the existence, uniqueness and stability of \({2\pi}\)-periodic solution of Duffing equation \({x'' + cx' + g(t, x) = h(t)}\) are presented. Moreover, the unique \({2\pi}\)-periodic solution is (exponentially asymptotically stable) and its rate of exponential decay c/2 is sharp. The new criterion characterizes \({g_{x}^{\prime}(t, x) - c^2/4}\) with L p -norms \({(p \in [1, \infty])}\), and the classical criterion employs the \({L^{\infty}}\)-norm. The advantage is that we can deal with the case that \({g_{x}^{\prime}(t, x) - c^2/4}\) is beyond the optimal bounds of the \({L^{\infty}}\)-norm, because of the difference between the L p -norm and the \({L^{\infty}}\)-norm. 相似文献
16.
Xiao Yi Zhang 《数学学报(英文版)》2008,24(6):891-900
In this short note, we show the illposedness of anisotropic Schroedinger equation in L^2 if the growth of nonlinearity is larger than a threshold power pc which is also the critical power for blowup, as Fibich, Ilan and Schochet have pointed out recently. The illposedness in anisotropic Sobolev space Hk,d-d^2s,s where 0 〈 s 〈 sc, sc =d/2-k/4-2/p-1, and the illposedness in Sobolev space of negative order H^s, s 〈 0 are also proved. 相似文献
17.
In a general unbounded uniform C 2-domain \({\Omega \subset \mathbb{R}^n, n \geq 3}\) , and \({1\leq q\leq \infty}\) consider the spaces \({\tilde{L}^q(\Omega)}\) defined by \({\tilde{L^q}(\Omega) := \left\{\begin{array}{ll}L^q(\Omega)+L^2(\Omega),\quad q < 2, \\ L^q(\Omega)\cap L^2(\Omega),\quad q\geq 2, \end{array}\right.}\) and corresponding subspaces of solenoidal vector fields, \({\tilde{L}^q_\sigma(\Omega)}\) . By studying the complex and real interpolation spaces of these we derive embedding properties for fractional order spaces related to the Stokes problem and L p ? L q -type estimates for the corresponding semigroup. 相似文献
18.
A. I. Kamzolov 《Moscow University Mathematics Bulletin》2007,62(4):158-162
Asymptotic estimates of L q -norms of partial sums of Fourier-Legendre series of functions from L p [?1; 1] are obtained. 相似文献
19.
On <Emphasis Type="Italic">c</Emphasis><Superscript>#</Superscript>-normal subgroups infinite groups
Huaquan Wei Qiao Dai Hualian Zhang Yubo Lv Liying Yang 《Frontiers of Mathematics in China》2018,13(5):1169-1178
A subgroup H of a finite group G is called a c#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is a CAP-subgroup of G: In this paper, we investigate the influence of fewer c#-normal subgroups of Sylow p-subgroups on the p-supersolvability, p-nilpotency, and supersolvability of finite groups. We obtain some new sufficient and necessary conditions for a group to be p-supersolvable, p-nilpotent, and supersolvable. Our results improve and extend many known results. 相似文献
20.
Expansive homoclinic classes of generic <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript>-vector fields
下载免费PDF全文
![点击此处可从《数学学报(英文版)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Let γ be a hyperbolic closed orbit of a C 1 vector field X on a compact C ∞ manifold M of dimension n ≥ 3, and let H X(γ) be the homoclinic class of X containing γ. In this paper, we prove that C 1-generically, if H X(γ) is expansive and isolated, then it is hyperbolic. 相似文献