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Zihua Guo Xingxing Liu Luc Molinet Zhaoyang Yin 《Journal of Differential Equations》2019,266(2-3):1698-1707
We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa–Holm equation, Degasperis–Procesi equation and Novikov equation etc., in the critical Sobolev space and even in the Besov space for . Our results cover both real-line and torus cases (only real-line case for Novikov), solving an open problem left in the previous works ([5], [14], [16]). 相似文献
3.
《Optimization》2012,61(5-6):361-385
We present three counterexamples related to the maximum principle for the time optimal problem. The system is linear, infinite dimensional, with point target and “full” control 相似文献
4.
洪勇 《数学年刊A辑(中文版)》2011,32(5):599-606
设核函数K(u,v)具有对称性和齐次性,对如下定义的奇异重积分算子T:(Tf)(y)=∫R_+~n K(‖x‖α,‖y‖α)f(x)dx,y∈R_+~n,其中‖x‖α=(x_1~α+…+x_n~α)~1/α(α>0),研究了T的范数及其应用. 相似文献
5.
Let X be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, via a new Cotlar type inequality linking commutators and corresponding maximal operators, a weighted Lp(X) estimate with general weights and a weak type endpoint estimate with A1(X) weights are established for maximal operators corresponding to commutators of BMO(X) functions and singular integral operators with non-smooth kernels. 相似文献
6.
On a Hilbert-type linear series operator and its applications 总被引:1,自引:0,他引:1
Jianjun Jin 《Journal of Mathematical Analysis and Applications》2010,371(2):691-704
This paper deals with a Hilbert-type linear series operator and its norm. Several generalizations of the Hilbert-type inequalities whose kernels are symmetric and homogeneous of the first order are presented. Included are applications of some new extended Hilbert-type inequalities with the best possible constant factors and the equivalent forms are established. Also, the reverse forms and some particular forms are obtained as special cases of the results of this paper. 相似文献
7.
In this paper we ask which norms on Md induced by an absolute vector norm are sub-multiplicative with respect to the Hadamard product. We provide a simple necessary condition for submultiplicativity. We demonstrate that each norm on Md induced by an lp norm Hadamard submultiplicative and that the norms induced by certain polyhedral norms are Hadamard submultiplicative. We also consider some related inequalities. 相似文献
8.
In this work we characterize normal invertible operators via inequalities with unitarily invariant norm of elementary operators. 相似文献
9.
Anthony To-Ming Lau 《Journal of Functional Analysis》2008,254(10):2513-2533
In this paper, we explore the properties of projections of norm one on general Banach algebras, in particular the relation with conditional expectations for algebras which arise in harmonic analysis. 相似文献
10.
The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the “convex feasibility” problem. This is the third paper in a series on a study of the rate of convergence for the cyclic projections algorithm. In the first of these papers, we showed that the rate could be described in terms of the “angles” between the convex sets involved. In the second, we showed that these angles often had a more tractable formulation in terms of the “norm” of the product of the (nonlinear) metric projections onto related convex sets.In this paper, we show that the rate of convergence of the cyclic projections algorithm is also intimately related to the “linear regularity property” of Bauschke and Borwein, the “normal property” of Jameson (as well as Bakan, Deutsch, and Li’s generalization of Jameson’s normal property), the “strong conical hull intersection property” of Deutsch, Li, and Ward, and the rate of convergence of iterated parallel projections. Such properties have already been shown to be important in various other contexts as well. 相似文献