Search results for "Bounded"
showing 10 items of 658 documents
Extension of a Schur theorem to groups with a central factor with a bounded section rank
2013
Abstract A well-known result reported by Schur states that the derived subgroup of a group is finite provided its central factor is finite. Here we show that if the p-section rank of the central factor of a locally generalized radical group is bounded, then so is the p-section rank of its derived subgroup. We also give an explicit expression for this bound.
On the number of conjugacy classes of zeros of characters
2004
Letm be a fixed non-negative integer. In this work we try to answer the following question: What can be said about a (finite) groupG if all of its irreducible (complex) characters vanish on at mostm conjugacy classes? The classical result of Burnside about zeros of characters says thatG is abelian ifm=0, so it is reasonable to expect that the structure ofG will somehow reflect the fact that the irreducible characters vanish on a bounded number of classes. The same question can also be posed under the weaker hypothesis thatsome irreducible character ofG hasm classes of zeros. For nilpotent groups we shall prove that the order is bounded by a function ofm in the first case but only the derive…
The Neumann Problem for the Total Variation Flow
2004
This chapter is devoted to prove existence and uniqueness of solutions for the minimizing total variation flow with Neumann boundary conditions, namely $$ \left\{ \begin{gathered} \frac{{\partial u}} {{\partial t}} = div\left( {\frac{{Du}} {{\left| {Du} \right|}}} \right) in Q = (0,\infty ) \times \Omega , \hfill \\ \frac{{\partial u}} {{\partial \eta }} = 0 on S = (0,\infty ) \times \partial \Omega , \hfill \\ u(0,x) = u_0 (x) in x \in \Omega , \hfill \\ \end{gathered} \right. $$ (2.1) where Ω is a bounded set in ℝ N with Lipschitz continuous boundary ∂ Ω and u0 ∈ L1(Ω). As we saw in the previous chapter, this partial differential equation appears when one uses the steepest descent method …
Some Aspects of Vector-Valued Singular Integrals
2009
Let A, B be Banach spaces and \(1 < p < \infty. \; T\) is said to be a (p, A, B)- CalderoLon–Zygmund type operator if it is of weak type (p, p), and there exist a Banach space E, a bounded bilinear map \(u: E \times A \rightarrow B,\) and a locally integrable function k from \(\mathbb{R}^n \times \mathbb{R}^n \backslash \{(x, x): x \in \mathbb{R}^n\}\) into E such that $$T\;f(x) = \int u(k(x, y), f(y))dy$$ for every A-valued simple function f and \(x \notin \; supp \; f.\)
The Bourgain property and convex hulls
2007
Let (Ω, Σ, μ) be a complete probability space and let X be a Banach space. We consider the following problem: Given a function f: Ω X for which there is a norming set B ⊂ BX * such that Zf,B = {x * ○ f: x * ∈ B } is uniformly integrable and has the Bourgain property, does it follow that f is Birkhoff integrable? It turns out that this question is equivalent to the following one: Given a pointwise bounded family ℋ ⊂ ℝΩ with the Bourgain property, does its convex hull co(ℋ) have the Bourgain property? With the help of an example of D. H. Fremlin, we make clear that both questions have negative answer in general. We prove that a function f: Ω X is scalarly measurable provided that there is a n…
Soluble groups with their centralizer factor groups of bounded rank
2007
Abstract For a group class X , a group G is said to be a C X -group if the factor group G / C G ( g G ) ∈ X for all g ∈ G , where C G ( g G ) is the centralizer in G of the normal closure of g in G . For the class F f of groups of finite order less than or equal to f , a classical result of B.H. Neumann [Groups with finite classes of conjugate elements, Proc. London Math. Soc. 1 (1951) 178–187] states that if G ∈ C F f , the commutator group G ′ belongs to F f ′ for some f ′ depending only on f . We prove that a similar result holds for the class S r ( d ) , the class of soluble groups of derived length at most d which have Prufer rank at most r . Namely, if G ∈ C S r ( d ) , then G ′ ∈ S d…
Doubly nonlinear equations with unbounded operators
2004
Abstract The solvability of the evolution system v′(t)+ B (t)u(t)∋ f (t),v(t)∈ A (t)u(t) , 0 A (t) are bounded, possibly degenerate, subdifferentials and B (t) are unbounded subdifferentials.
A variation on theorems of Jordan and Gluck
2006
Abstract Gluck proved that any finite group G has an abelian subgroup A such that | G : A | is bounded by a polynomial function of the largest degree of the complex irreducible characters of G . This improved on a previous bound of Isaacs and Passman. In this paper, we present a variation of this result that looks at the number of prime factors. All these results, in turn, may be seen as variations on the classical theorem of Jordan on linear groups.
Complete weights andv-peak points of spaces of weighted holomorphic functions
2006
We examine the geometric theory of the weighted spaces of holomorphic functions on bounded open subsets ofC n ,C n ,H v (U) and\(H_{v_o } (U)\), by finding a lower bound for the set of weak*-exposed and weak*-strongly exposed points of the unit ball of\(H_{v_o } (U)'\) and give necessary and sufficient conditions for this set to be naturally homeomorphic toU. We apply these results to examine smoothness and strict convexity of\(H_{v_o } (U)\) and\(H_v (U)\). We also investigate whether\(H_{v_o } (U)\) is a dual space.
Commutators of linear and bilinear Hilbert transforms
2003
Let α ∈ R \alpha \in \mathbb {R} , and let H α ( f , g ) ( x ) = 1 π p . v . ∫ f ( x − t ) g ( x − α t ) d t t H_\alpha (f,g)(x)=\frac {1}{\pi } p.v. \int f(x-t)g(x-\alpha t)\frac {dt}{t} and H f ( x ) = 1 π p . v . ∫ f ( x − t ) d t t Hf(x)= \frac {1}{\pi } p.v.\int f(x-t)\frac {dt}{t} denote the bilinear and linear Hilbert transforms, respectively. It is proved that, for 1 > p > ∞ 1>p>\infty and α 1 ≠ α 2 \alpha _1\ne \alpha _2 , H α 1 − H α 2 H_{\alpha _1}-H_{\alpha _2} maps L p × B M O L^p\times BMO into L p L^{p} and it maps B M O × L p BMO \times L^p into L p L^{p} if and only if sign ( α 1 ) = sign ( α 2 ) \operatorname {sign}(\alpha _1)=\operatorname {sign}(\alpha _2…