Search results for "maximal"

Self-improvement of weighted pointwise inequalities on open sets

2020

We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincar\'e and $p$-Hardy weights for an open set $\Omega\subset X$, where $X$ is a metric measure space. We also apply the self-improvement of weighted pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.

A maximal Function Approach to Two-Measure Poincaré Inequalities

2018

This paper extends the self-improvement result of Keith and Zhong in  Keith and Zhong (Ann. Math. 167(2):575–599, 2008) to the two-measure case. Our main result shows that a two-measure (p, p)-Poincare inequality for $$10$$ under a balance condition on the measures. The corresponding result for a maximal Poincare inequality is also considered. In this case the left-hand side in the Poincare inequality is replaced with an integral of a sharp maximal function and the results hold without a balance condition. Moreover, validity of maximal Poincare inequalities is used to characterize the self-improvement of two-measure Poincare inequalities. Examples are constructed to illustrate the role of t…

Functions of One Variable

2019

A classical result of Fatou gives that every bounded holomorphic function on the disc has radial limits for almost every point in the torus, and the limit function belongs to the Hardy space H_\infty of the torus. This property is no longer true when we consider vector-valued functions. The Banach spaces X for which this property is satisfied are said to have the analytic Radon-Nikodym property (ARNP). Some important equivalent reformulations of ARNP are studied in this chapter. Among others, X has ARNP if and only if each X-valued H_p- function f on the disc has radial limits almost everywhere on the torus (and not only H_\infty-functions). Even more, in this case each such f has non-tange…

Evidences of cannabinoids-induced modulation of paroxysmal events in an experimental model of partial epilepsy in the rat

2010

Different studies have been shown a clear anticonvulsant activity exerted by cannabinoids (CB) through the CB1 receptor activation. The purpose of this study was to evaluate, in an in vivo experimental model of temporal lobe epilepsy (maximal dentate gyrus activation - MDA) in the rat, the protective effect of (R)-(+)-[2,3-Dihydro-5-methyl-3-(4-morpholinylmethyl) pyrrolo[1,2,3-de]-1,4-benzoxazin-6-Yl]-1-naphthalenylmethanone (WIN 55,212-2, CB agonist) alone or in combination with N-(piperidin-1-yl)-5-(4-iodophenyl)-1-(2,4-dichlorophenyl)-4-methyl-1H-pyrazole-3-carboxamide (AM251, selective CB1 antagonist). Pre-treatment with AM251 (1 mg kg-1, 30 min interval) dramatically reduced the signif…

2015

It has been shown that the mental fatigue induced by prolonged self-regulation increases perception of effort and reduces performance during subsequent endurance exercise. However, the physiological mechanisms underlying these negative effects of mental fatigue are unclear. The primary aim of this study was to test the hypothesis that mental fatigue exacerbates central fatigue induced by whole-body endurance exercise. Twelve subjects performed 30 min of either an incongruent Stroop task to induce a condition of mental fatigue or a congruent Stroop task (control condition) in a random and counterbalanced order. Both cognitive tasks (CTs) were followed by a whole-body endurance task (ET) cons…

Cardiovascular and Autonomic Responses to a Maximal Exercise Test in Elite Youngsters

2017

AbstractTo analyze cardiovascular and autonomic responses in elite youngsters, 13 male cyclists (15.43±0.51 years) performed a graded-test until voluntary exhaustion. Oxygen consumption (VO2), blood lactate (BLa), arterial oxygen saturation (SaO2), respiratory exchange ratio (RER) and rating of perceived exertion (RPE) were collected, while heart rate (HR) was registered for heart rate variability (HRV) analyses, looking for linear and nonlinear comparisons. Cyclists reached maximal exertion [RPE: 19.14±0.94; BLa: 8.92±2.51 mmol.L−1; RER: 1.04±0.03; SaO2: 92.43±2.5%] and high-level performance (4.41±0.46 W·Kg−1; 60.77±6.87 ml·Kg·min−1) once over 95% of age-predicted HRmax. VO2 and RPE incre…

Existence and Relaxation Results for Second Order Multivalued Systems

2021

AbstractWe consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have the combined effects of a maximal monotone term $A(x)$ A ( x ) and of a multivalued perturbation $F(t,x,y)$ F ( t , x , y ) which can be convex or nonconvex valued. We consider the cases where $D(A)\neq \mathbb{R}^{N}$ D ( A ) ≠ R N and $D(A)= \mathbb{R}^{N}$ D ( A ) = R N and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.

Well-behaved *-Representations

2002

This chapter is devoted to the study of the so-called well-behaved *-representations of (partial) *-algebras. Actually one may define are two notions of well-behavedness and we will discuss the relation between them. These notions are introduced in order to avoid pathologies which may arise for general *-representations and to select “nice” representations, which may have a richer theory. In Section 8.1, we construct a class {π p } of *-representations, starting from an unbounded C*-seminorm p and we define nice *-representations in {π p }, called well-behaved. We also characterize their existence. In Section 8.2, we introduce the well-behaved *-representations associated with a compatible …

Effects of strength training on muscle power and serum hormones in middle-aged and older men.

2001

Effects of 16-wk strength training on maximal strength and power performance of the arm and leg muscles and serum concentrations [testosterone (T), free testosterone (FT), and cortisol] were examined in 11 middle-aged (M46; 46 ± 2 yr) and 11 older men (M64; 64 ± 2 yr). During the 16-wk training, the relative increases in maximal strength and muscle power output of the arm and leg muscles were significant in both groups ( P < 0.05–0.001), with no significant differences between the two groups. The absolute increases were higher ( P < 0.01–0.05) in M46 than in M64 mainly during the last 8 wk of training. No significant changes were observed for serum T and FT concentrations. Analysis o…

Maximal subgroups and formations

1989

Abstract We define, in each finite group G , some subgroups of Frattini-type in relation with a saturated formation and with a set of primes and study their properties, especially their influence in the structure of G .