Search results for "maximal"

On the regularity of the Hardy-Littlewood maximal operator on subdomains of ℝn

2010

AbstractWe establish the continuity of the Hardy-Littlewood maximal operator on W1,p(Ω), where Ω ⊂ ℝn is an arbitrary subdomain and 1 < p < ∞. Moreover, boundedness and continuity of the same operator is proved on the Triebel-Lizorkin spaces Fps,q (Ω) for 1 < p,q < ∞ and 0 < s < 1.

Estimates of maximal functions measuring local smoothness

1999

Letη be a nondecreasing function on (0, 1] such thatη(t)/t decreases andη(+0)=0. Letf ∈L(I n ) (I≡[0,1]. Set $${\mathcal{N}}_\eta f(x) = \sup \frac{1}{{\left| Q \right|\eta (\left| Q \right|^{1/n} )}} \smallint _Q \left| {f(t) - f(x)} \right|dt,$$ , where the supremum is taken over all cubes containing the pointx. Forη=t α (0<α≤1) this definition was given by A.Calderon. In the paper we prove estimates of the maximal functions $${\mathcal{N}}_\eta f$$ , along with some embedding theorems. In particular, we prove the following Sobolev type inequality: if $$1 \leqslant p< q< \infty , \theta \equiv n(1/p - 1/q)< 1, and \eta (t) \leqslant t^\theta \sigma (t),$$ , then $$\parallel {\mathcal{N}}_…

Maximal potentials, maximal singular integrals, and the spherical maximal function

2014

We introduce a notion of maximal potentials and we prove that they form bounded operators from L to the homogeneous Sobolev space Ẇ 1,p for all n/(n − 1) < p < n. We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces.

Continuity of the maximal operator in Sobolev spaces

2006

We establish the continuity of the Hardy-Littlewood maximal operator on Sobolev spaces W 1,p (R n ), 1 < p < ∞. As an auxiliary tool we prove an explicit formula for the derivative of the maximal function.

REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION

2003

The purpose of this work is to show that the fractional maximal operator has somewhat unexpected regularity properties. The main result shows that the fractional maximal operator maps -spaces boundedly into certain first-order Sobolev spaces. It is also proved that the fractional maximal operator preserves first-order Sobolev spaces. This extends known results for the Hardy–Littlewood maximal operator.

Maximal Function Methods for Sobolev Spaces

2021

The impact of spatial correlation on the statistical properties of the capacity of nakagami-m channels with MRC and EGC

2011

Published version of an article published in the journal: EURASIP Journal on Wireless Communications and Networking. Also available from the publisher at: http://dx.doi.org/10.1186/1687-1499-2011-116. OA In this article, we have studied the statistical properties of the instantaneous channel capacitya of spatially correlated Nakagami-m channels for two different diversity combining methods, namely maximal ratio combining (MRC) and equal gain combining (EGC). Specifically, using the statistical properties of the instantaneous signal-to-noise ratio, we have derived the analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rat…

The influence of severity of fading on the statistical properties of the capacity of Nakagami-m channels with MRC and EGC

2010

In this article, we have studied the statistical properties of the capacity of Nakagami-m channels when spatial diversity combining, such as maximal ratio combining (MRC) and equal gain combining (EGC), is employed at the receiver. The presented results provide insight into the statistical properties of the channel capacity under a wide range of fading conditions in wireless links using L-branch diversity combining techniques. We have derived closed-form analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity. The statistical properties of the capacity ar…

Respiratory Muscle Strengths and Their Association with Lean Mass and Handgrip Strengths in Older Institutionalized Individuals

2020

The study of reduced respiratory muscle strengths in relation to the loss of muscular function associated with ageing is of great interest in the study of sarcopenia in older institutionalized individuals. The present study assesses the association between respiratory muscle parameters and skeletal mass content and strength, and analyzes associations with blood cell counts and biochemical parameters related to protein, lipid, glucose and ion profiles. A multicenter cross-sectional study was performed among patients institutionalized in nursing homes. The respiratory muscle function was evaluated by peak expiratory flow, maximal respiratory pressures and spirometry parameters, and skeletal m…

Physiotherapy Intervention for Preventing the Respiratory Muscle Deterioration in Institutionalized Older Women With Functional Impairment

2013

Abstract Introduction In elderly seniors (>80 years), respiratory function may be compromised when, in addition to the presence of comorbidity and loss of mobility, there is also reduced respiratory muscle (RM) strength. The literature has shown that RM training could be an effective method to improve RM function and prevent clinical deterioration, particularly in population with RM weakness. The main purpose of this paper was to assess the effectiveness of RM training on the respiratory muscle strength and endurance of institutionalized elderly women with functional impairment. Method Fifty-four residents (mean=85 years, SD=6.7) were randomly assigned to either a control (n=27) or training…