and Applied Analysis 3 Moreover, ∥Hωf∥Lp Rn →Lp Rn A. 1.7 Remark 1.1. Notice that the condition 1.6 implies that ω is integrable on 0, 1 since ∫1 0 ω t dt ≤ ∫1 0 t −n/pω t dt. We naturally assumeω is integrable on 0, 1 throughout this paper. Obviously, Theorem A implies the celebrated result of Hardy et al. 6, Theorem 329 , namely, for all 0 < α < 1 and 1 < p < ∞, ‖Iα‖Lp dx →Lp x−pαdx Γ ( 1 − 1...

In this paper we consider the quasilinear elliptic system ∆pu = uv, ∆pv = uv in a smooth bounded domain Ω ⊂ R , with the boundary conditions u = v = +∞ on ∂Ω. The operator ∆p stands for the p-Laplacian defined by ∆pu = div(|∇u|p−2∇u), p > 1, and the exponents verify a, e > p − 1, b, c > 0 and (a − p + 1)(e − p + 1) ≥ bc. We analyze positive solutions in both components, providing necessary and ...

Longitudinal change in five cognitive abilities was investigated to determine if the direction or magnitude of change was related to the individual's ability level. Adults between 18 and 97 years of age performed three versions of 16 cognitive tests on two occasions separated by an average of 2.7 years. In order to control for influences associated with regression toward the mean, level of abil...

Assessing cognitive change in older adults is a common use of neuropsychological services, and neuropsychologists have utilized several strategies to determine if a change is "real," "reliable," and "meaningful." Although standardized regression-based (SRB) prediction formulas may be useful in determining change, SRBs have not been widely applied to older adults. The current study sought to dev...

It is widely recognized that experience with cognitive tests can influence estimates of cognitive change. Prior research has estimated experience effects at the level of groups by comparing the performance of a group of participants tested for the second time with the performance of a different group of participants at the same age tested for the first time. This twice-minus-once-tested method ...

Does personality change across the entire life course, and are those changes due to intrinsic maturation or major life experiences? This longitudinal study investigated changes in the mean levels and rank order of the Big Five personality traits in a heterogeneous sample of 14,718 Germans across all of adulthood. Latent change and latent moderated regression models provided 4 main findings: Fir...