Search results for "Hardy"
showing 10 items of 61 documents
F-contractions of Hardy–Rogers-type and application to multistage decision
2016
We prove fixed point theorems for F-contractions of Hardy–Rogers type involving self-mappings defined on metric spaces and ordered metric spaces. An example and an application to multistage decision processes are given to show the usability of the obtained theorems.
Examples of Indexed PIP-Spaces
2009
This chapter is devoted to a detailed analysis of various concrete examples of pip-spaces. We will explore sequence spaces, spaces of measurable functions, and spaces of analytic functions. Some cases have already been presented in Chapters 1 and 2. We will of course not repeat these discussions, except very briefly. In addition, various functional spaces are of great interest in signal processing (amalgam spaces, modulation spaces, Besov spaces, coorbit spaces). These will be studied systematically in a separate chapter (Chapter 8).
Norm estimates for operators from Hp to ℓq
2008
Abstract We give upper and lower estimates of the norm of a bounded linear operator from the Hardy space H p to l q in terms of the norm of the rows and the columns of its associated matrix in certain vector-valued sequence spaces.
TP53 codon 72 polymorphism and cervical cancer
2009
Background Cervical cancer is caused primarily by human papillomaviruses (HPV). The polymorphism rs1042522 at codon 72 of the TP53 tumour-suppressor gene has been investigated as a genetic cofactor. More than 80 studies were done between 1998 and 2006, after it was initially reported that women who are homozygous for the arginine allele had a risk for cervical cancer seven times higher than women who were heterozygous for the allele. However, results have been inconsistent. Here we analyse pooled data from 49 studies to determine whether there is an association between TP53 codon 72 polymorphism and cervical cancer.Methods Individual data on 7946 cases and 7888 controls from 49 different st…
Atomic Decomposition of Weighted Besov Spaces
1996
We find the atomic decomposition of functions in the weighted Besov spaces under certain factorization conditions on the weight. Introduction. After achieving the atomic decomposition of Hardy spaces (see [8,22, 33]), many of the function saces have been shown to admit similar decompositions. Let us mention the decomposition of B.M.O. (see [32, 25]), Bergman spaces (see [9, 23]), the predual of Bloch space (see [ 11]), Besov spaces (see [15, 4, 10]), Lipschitz spaces (see [18]), Triebel-Lizorkin spaces (see [16, 31]),... They are obtained by quite different methods, but there is a unified and beautiful approach to get the decomposition for most of the spaces. This is the use of a formula du…
Uniqueness of diffusion on domains with rough boundaries
2016
Let $\Omega$ be a domain in $\mathbf R^d$ and $h(\varphi)=\sum^d_{k,l=1}(\partial_k\varphi, c_{kl}\partial_l\varphi)$ a quadratic form on $L_2(\Omega)$ with domain $C_c^\infty(\Omega)$ where the $c_{kl}$ are real symmetric $L_\infty(\Omega)$-functions with $C(x)=(c_{kl}(x))>0$ for almost all $x\in \Omega$. Further assume there are $a, \delta>0$ such that $a^{-1}d_\Gamma^{\delta}\,I\le C\le a\,d_\Gamma^{\delta}\,I$ for $d_\Gamma\le 1$ where $d_\Gamma$ is the Euclidean distance to the boundary $\Gamma$ of $\Omega$. We assume that $\Gamma$ is Ahlfors $s$-regular and if $s$, the Hausdorff dimension of $\Gamma$, is larger or equal to $d-1$ we also assume a mild uniformity property for $\Omega$ i…
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 \(x \notin \; supp \; f.\)
${\cal H}^1$ -estimates of Jacobians by subdeterminants
2002
Let $f:\Omega \rightarrow{\Bbb R}^n$ be a mapping in the Sobolev space $W^{1,n-1}_{loc}(\Omega,{\Bbb R}^n), n\geq 2$ . We assume that the cofactors of the differential matrix Df(x) belong to $L^\frac{n}{n-1}(\Omega)$ . Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space ${\cal H}^1(\Omega)$ .
Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential
2016
Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations
Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential
2016
Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations −Δpu − μ |x| p |u| p−2 u + m|u| p−2 u = f(u), x ∈ RN , where 1 0 and f is a continuous function. peerReviewed