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51.
We study the fully inhomogeneous Dirichlet problem for the Laplacian in bounded convex domains in Rn, when the size/smoothness of both the data and the solution are measured on scales of Besov and Triebel-Lizorkin spaces. As a preamble, we deal with the Dirichlet and Regularity problems for harmonic functions in convex domains, with optimal nontangential maximal function estimates. As a corollary, sharp estimates for the Green potential are obtained in a variety of contexts, including local Hardy spaces. A substantial part of this analysis applies to bounded semiconvex domains (i.e., Lipschitz domains satisfying a uniform exterior ball condition). 相似文献
52.
The aim of this paper is to introduce the notion of ergodic shadowing for a continuous onto map which is equivalent to the map being topologically mixing and has the ordinary shadowing property. In particular, we deduce the chaotic behavior of a map with ergodic shadowing property. Moreover, we define some kind of specification property and investigate its relation to the ergodic shadowing property. 相似文献
53.
E. Durand-Cartagena 《Journal of Mathematical Analysis and Applications》2010,363(2):525-548
For a metric space X, we study the space D∞(X) of bounded functions on X whose pointwise Lipschitz constant is uniformly bounded. D∞(X) is compared with the space LIP∞(X) of bounded Lipschitz functions on X, in terms of different properties regarding the geometry of X. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare D∞(X) with the Newtonian-Sobolev space N1,∞(X). In particular, if X supports a doubling measure and satisfies a local Poincaré inequality, we obtain that D∞(X)=N1,∞(X). 相似文献
54.
朱诗红 《数学的实践与认识》2010,40(1)
设BδA,*是由Bochner-Riesz算子生成的极大多线性Bochner-Riesz算子,其中DγA∈Λ.β(γ=m).我们得到了在一定条件下,极大多线性Bochner-Riesz算子在Triebel-Lizorkin空间中的有界性. 相似文献
55.
With the newly developed octonion analytic function theory, we confirm the octonionic analogue of the Calderón's conjecture. As application, we obtain the Plemelj formula in octonionic space. 相似文献
56.
Livinus U. Uko 《Journal of Mathematical Analysis and Applications》2008,342(2):909-914
The Kantorovich theorem is a fundamental tool in nonlinear analysis for proving the existence and uniqueness of solutions of nonlinear equations arising in various fields. This theorem was weakened recently by Argyros who used a combination of Lipschitz and center-Lipschitz conditions in place of the Lipschitz conditions of the Kantorovich theorem. In the present paper we prove a weak Kantorovich-type theorem that gives the same conclusions as the previous two results under weaker conditions. Illustrative examples are provided in the paper. 相似文献
57.
Aline Bonami Sandrine Grellier Mohammad Kacim 《Transactions of the American Mathematical Society》2008,360(3):1377-1390
We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are still bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.
58.
Luděk Zajíček 《Czechoslovak Mathematical Journal》2008,58(3):849-864
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space and properties of generated σ-ideals are studied. These σ-ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we
improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of
convex functions. 相似文献
59.
Shahar Mendelson 《Random Structures and Algorithms》2005,27(1):25-45
We investigate a new notion of embedding of subsets of {?1,1}n in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, …, n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that even when considering “small” subsets of {?1, 1}n, the vast majority of such sets do not embed in a better way than the entire cube in any normed space that satisfies a minor structural assumption. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005 相似文献
60.
Min Wu 《Journal of Mathematical Analysis and Applications》2008,339(2):1425-1431
We provide sufficient conditions for the convergence of the Newton-like methods in the assumption that the derivative satisfies some kind of weak Lipschitz conditions. Consequently, some important convergence theorems follow from our main result in this paper. 相似文献