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41.
We study graphs defined on families of finite sets of natural numbers and their chromatic properties. Of particular interest are graphs for which the edge relation is given by the shift. We show that when considering shift graphs with infinite chromatic number, one can center attention on graphs defined on precompact thin families. We define a quasi-order relation on the collection of uniform families defined in terms of homomorphisms between their corresponding shift graphs, and show that there are descending -sequences. Specker graphs are also considered and their relation with shift graphs is established. We characterize the family of Specker graphs which contain a homomorphic image of a shift graph. 相似文献
42.
43.
Stevo Stevi? 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2448-2454
Bergman-Privalov class ANα(B) consists of all holomorphic functions on the unit ball B⊂Cn such that
‖f‖ANα:=∫Bln(1+∣f(z)∣)dVα(z)<∞, 相似文献
44.
A complete Boolean algebra
\mathbbB{\mathbb{B}}satisfies property ((h/2p)){(\hbar)}iff each sequence x in
\mathbbB{\mathbb{B}}has a subsequence y such that the equality lim sup z
n
= lim sup y
n
holds for each subsequence z of y. This property, providing an explicit definition of the a posteriori convergence in complete Boolean algebras with the sequential
topology and a characterization of sequential compactness of such spaces, is closely related to the cellularity of Boolean
algebras. Here we determine the position of property ((h/2p)){(\hbar)}with respect to the hierarchy of conditions of the form κ-cc. So, answering a question from Kurilić and Pavlović (Ann Pure Appl Logic 148(1–3):49–62, 2007), we show that ${``\mathfrak{h}{\rm -cc}\Rightarrow (\hbar)"}${``\mathfrak{h}{\rm -cc}\Rightarrow (\hbar)"}is not a theorem of ZFC and that there is no cardinal
\mathfrakk{\mathfrak{k}}, definable in ZFC, such that ${``\mathfrak{k} {\rm -cc} \Leftrightarrow (\hbar)"}${``\mathfrak{k} {\rm -cc} \Leftrightarrow (\hbar)"}is a theorem of ZFC. Also, we show that the set { k: each k-cc c.B.a. has ((h/2p) ) }{\{ \kappa : {\rm each}\, \kappa{\rm -cc\, c.B.a.\, has}\, (\hbar ) \}}is equal to
[0, \mathfrakh){[0, \mathfrak{h})}or
[0, \mathfrak h]{[0, {\mathfrak h}]}and that both values are consistent, which, with the known equality
{k: each c.B.a. having ((h/2p) ) has the k-cc } = [\mathfrak s, ¥){{\{\kappa : {\rm each\, c.B.a.\, having }\, (\hbar )\, {\rm has\, the}\, \kappa {\rm -cc } \} =[{\mathfrak s}, \infty )}}completes the picture. 相似文献
45.
We study the following two integral operators where g is an analytic function on the open unit disk in the complex plane. The boundedness and compactness of these two operators between the α ‐Bloch space Bα and the Besov space are discussed in this paper (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
46.
Stevo Stević 《Siberian Mathematical Journal》2009,50(1):167-180
We study the compactness of the Hardy-Littlewood operator on several spaces of harmonic functions on the unit ball in ? n such as: a-Bloch, weighted Hardy, weighted Bergman, Besov, BMO p , and Dirichlet spaces. 相似文献
47.
We prove that an analytic function f on the unit ball B with Hadamard gaps, that is, (the homogeneous polynomial expansion of f) satisfying nk+1/nk?λ>1 for all k∈N, belongs to the space if and only if . Moreover, we show that the following asymptotic relation holds . Also we prove that limr→1(1-r2)α‖Rfr‖p=0 if and only if . These results confirm two conjectures from the following recent paper [S. Stevi?, On Bloch-type functions with Hadamard gaps, Abstr. Appl. Anal. 2007 (2007) 8 pages (Article ID 39176)]. 相似文献
48.
Stevo Todorcevic 《Israel Journal of Mathematics》1985,52(1-2):53-58
A kind ofk
+-Aronszajn tree is used to construct some strong negative partition relations onk
+. 相似文献
49.
Motivated by the notion of Ulam’s type stability and some recent results of S.-M. Jung, concerning the stability of zeros of polynomials, we prove a stability result for functional equations that have polynomial forms, considerably improving the results in the literature. 相似文献
50.