A characterization of some weighted inequalities for the vector-valued weighted maximal function

2010 ◽  
Vol 26 (11) ◽  
pp. 2191-2198 ◽  
Author(s):  
Cui Lan Wu
Keyword(s):  
Maximal Function ◽  
Weighted Inequalities ◽  
Vector Valued

scholarly journals Weighted inequalities for a vector-valued strong maximal function

1988 ◽  
Vol 18 (3) ◽  
pp. 565-570 ◽  
Author(s):  
O.N. Capri ◽  
C.E. Gutierrez
Keyword(s):  
Maximal Function ◽  
Weighted Inequalities ◽  
Vector Valued

scholarly journals Hardy Spaces on Homogeneous Groups and Littlewood-Paley Functions

2020 ◽  
Vol 71 (1) ◽  
pp. 295-320
Author(s):  
Shuichi Sato
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Homogeneous Groups ◽  
Peetre Maximal Function ◽  
Vector Valued

Abstract We establish a characterization of the Hardy spaces on the homogeneous groups in terms of the Littlewood–Paley functions. The proof is based on vector-valued inequalities shown by applying the Peetre maximal function.

A macroscopic theory of microcrack growth in brittle materials

1991 ◽  
Vol 335 (1639) ◽  
pp. 455-485 ◽  
Keyword(s):  
Crack Growth ◽  
Brittle Materials ◽  
Macroscopic Theory ◽  
Rate Of Increase ◽  
Inelastic Behaviour ◽  
Constitutive Response ◽  
Macroscopic Plasticity ◽  
Microcrack Growth ◽  
Vector Valued

This paper is concerned with the development of a macroscopic theory of crack growth in fairly brittle materials. Average characteristics of the cracks are described in terms of an additional vector-valued variable in the macroscopic theory, which is determined by an additional momentum-like balance law associated with the rate of increase of the area of the cracks and includes the effects of forces maintaining the crack growth and the inertia of microscopic particles surrounding the cracks. The basic developments represent an idealized characterization of inelastic behaviour in the presence of crack growth, which accounts for energy dissipation without explicit use of macroscopic plasticity effects. A physically plausible constraint on the rate of crack growth is adopted to simplify the theory. To ensure that the results of the theory are physically reasonable, the constitutive response of the dependent variables are significantly restricted by consideration both of the energetic effects and of the microscopic processes that give rise to crack growth. These constitutive developments are in conformity with many of the standard results and observations reported in the literature on fracture mechanics. The predictive nature of the theory is illustrated with reference to two simple examples concerning uniform extensive and compressive straining.

Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators

2015 ◽  
Vol 67 (5) ◽  
pp. 1161-1200 ◽  
Author(s):  
Junqiang Zhang ◽  
Jun Cao ◽  
Renjin Jiang ◽  
Dachun Yang
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic Operator ◽  
Muckenhoupt Class ◽  
Degenerate Elliptic ◽  
Function Characterization

AbstractLet w be either in the Muckenhoupt class of A2(ℝn) weights or in the class of QC(ℝn) weights, and let be the degenerate elliptic operator on the Euclidean space ℝn, n ≥ 2. In this article, the authors establish the non-tangential maximal function characterization of the Hardy space associated with , and when with , the authors prove that the associated Riesz transform is bounded from to the weighted classical Hardy space .

scholarly journals Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianfeng Dong ◽  
Jizheng Huang ◽  
Heping Liu
Keyword(s):  
Molecular Characterization ◽  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Hardy Type ◽  
Type Spaces ◽  
Reverse Hölder

LetL=-Δ+Vbe a Schrödinger operator onRn,n≥3, whereV≢0is a nonnegative potential belonging to the reverse Hölder classBn/2. The Hardy type spacesHLp, n/(n+δ) <p≤1,for someδ>0, are defined in terms of the maximal function with respect to the semigroup{e-tL}t>0. In this paper, we investigate the bounded properties of some singular integral operators related toL, such asLiγand∇L-1/2, on spacesHLp. We give the molecular characterization ofHLp, which is used to establish theHLp-boundedness of singular integrals.

scholarly journals A note on bi-contractive projections on spaces of vector valued continuous functions

2018 ◽  
Vol 5 (1) ◽  
pp. 42-49
Author(s):  
Fernanda Botelho ◽  
T.S.S.R.K. Rao
Keyword(s):  
Hilbert Space ◽  
Continuous Functions ◽  
Choquet Simplex ◽  
Contractive Projections ◽  
Vector Valued

Abstract This paper concerns the analysis of the structure of bi-contractive projections on spaces of vector valued continuous functions and presents results that extend the characterization of bi-contractive projections given by the first author. It also includes a partial generalization of these results to affine and vector valued continuous functions from a Choquet simplex into a Hilbert space.

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