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1 – 10 of 137Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based on a complete orthonormal system of Dunkl kernels generalizing the classical…
Abstract
Purpose
Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based on a complete orthonormal system of Dunkl kernels generalizing the classical exponential system defining the classical Fourier series.
Design/methodology/approach
Although the difficulties related to the Dunkl settings, the techniques used by K. Sato were still efficient in this case to establish the inequalities which have expected similarities with the classical case, and Hardy and Paley theorems for the Fourier–Bessel expansions due to the fact that the Bessel transform is the even part of the Dunkl transform.
Findings
Paley's inequality and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions.
Research limitations/implications
This work is a participation in extending the harmonic analysis associated with the Dunkl operators and it shows the utility of BMO spaces to establish some analytical results.
Originality/value
Dunkl theory is a generalization of Fourier analysis and special function theory related to root systems. Establishing Paley and Hardy's inequalities in these settings is a participation in extending the Dunkl harmonic analysis as it has many applications in mathematical physics and in the framework of vector valued extensions of multipliers.
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Constructive deviance has received increasing attention across the last 20 years. However, because the distinction between constructive and traditional forms of deviance (i.e.…
Abstract
Constructive deviance has received increasing attention across the last 20 years. However, because the distinction between constructive and traditional forms of deviance (i.e., destructive) is based on the intent behind the behaviors, it can be difficult to determine which acts are constructive. As an umbrella construct consisting of several forms of deviant acts (e.g., whistle-blowing, employee voice, necessary evils), research into constructive deviance has largely remained focused on the individual behaviors to date. While advancements have been made, this focus has limited the consideration of an overarching understanding of constructive deviance in the workplace. Further, constructs like constructive deviance that straddle the bounds between beneficial and detrimental necessitate the exploration into their antecedents as determined by the employees (i.e., apples), their environments (e.g., barrels), or some combination of the two. The author seeks to advance the research in constructive deviance by proposing a testable model. In which, the author develops an interactionist perspective of the antecedents to reposition constructive deviance as the acts of good employees in restrictive or negative environments. In doing so, the author considers how various aspects of individuals, their organizational environments, and the influence of their leaders interact. The author then develops a multi-stakeholder approach to the outcomes of constructive deviance to consider how the various parties (i.e., organization, coworkers, customers) are expected to respond and how these responses impact the more distal outcomes as well as the likelihood of engaging in future constructive deviance.
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