Search results for "Maxima"

Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces

2013

Motivated by the results of Korry, and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajlasz spaces, Hajlasz-Besov, and Hajlasz-Triebel-Lizorkin spaces on metric measure spaces. We show that the discrete fractional maximal operator maps these spaces to the spaces of the same type with higher smoothness. Our results extend and unify aforementioned results. We present our results in a general setting, but they are new already in the Euclidean case.

Self-improvement of pointwise Hardy inequality

2019

We prove the self-improvement of a pointwise p p -Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.

Doubly nonlinear periodic problems 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 t T , with the periodic condition v (0)= v ( T ) is investigated in the case where A (t) are bounded, possibly degenerate, subdifferentials and B (t) are unbounded subdifferentials.

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…

Difficulties of density functional theory in predicting the torsional potential of 2,2?-bithiophene

1998

The internal rotation of 2,2′-bithiophene was investigated within the density functional theory (DFT) approach. Fully optimized DFT torsional potentials are compared with Moller–Plesset (MP2) results which predict a fourfold potential with s-cis- and s-trans-gauche minima. DFT calculations fail in describing the energetics of the internal rotation because they favor planar vs. perpendicular conformers. Gradient-corrected functionals provide torsional potentials where the gauche minima have almost vanished and the s-ciss-trans interconversion barriers are twice as high as the barriers obtained at the MP2 level. The use of local functionals augments the shortcomings of the DFT approach. The g…

Improved moment scaling estimation for multifractal signals

2018

A fundamental problem in the analysis of multifractal processes is to estimate the scaling exponent K(q) of moments of different order q from data. Conventional estimators use the empirical moments μ^[subscript r][superscript q]=⟨ | ε[subscript r](τ)|[superscript q]⟩ of wavelet coefficients ε[subscript r](τ), where τ is location and r is resolution. For stationary measures one usually considers "wavelets of order 0" (averages), whereas for functions with multifractal increments one must use wavelets of order at least 1. One obtains K^(q) as the slope of log(μ^[subscript r][superscript q]) against log(r) over a range of r. Negative moments are sensitive to measurement noise and quantization.…

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…