Search results for "Bounded function"

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 &gt; p &gt; ∞ 1&gt;p&gt;\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…

Local Total Variation Bounded Methods for Hyperbolic Conservation Laws

2003

Finite element analysis of varitional crimes for a quasilinear elliptic problem in 3D

2000

We examine a finite element approximation of a quasilinear boundary value elliptic problem in a three-dimensional bounded convex domain with a smooth boundary. The domain is approximated by a polyhedron and a numerical integration is taken into account. We apply linear tetrahedral finite elements and prove the convergence of approximate solutions on polyhedral domains in the $W^1_2$ -norm to the true solution without any additional regularity assumptions.

Third-order iterative methods without using any Fréchet derivative

2003

AbstractA modification of classical third-order methods is proposed. The main advantage of these methods is they do not need to evaluate any Fréchet derivative. A convergence theorem in Banach spaces, just assuming the second divided difference is bounded and a punctual condition, is analyzed. Finally, some numerical results are presented.