Abstract. We prove that if f : I ⊂ R → R is of bounded variation, then the uncentered maximal function Mf is absolutely continuous, and its derivative satisfies the sharp inequality DM f L 1 (I) ≤ |Df |(I). This allows us to obtain, under less regularity, versions of classical inequalities involving derivatives.

Sustainability is a field of growing interest in Project Management (PM). Literature on Sustainability in PM is abundant at a theoretical level; however, it is necessary to explore hands-on approaches for designing models and practices. The purpose of this study is to introduce management systems as a practical tool for Sustainability in PM. Management system certifications are used as an indicator of the implementation of Sustainability practices, and thus, the impact of Sustainability on the success of projects is analyzed. The methodology for this study includes the analysis of the correspondence between Sustainability and five recognized management system standards (ISO 9001, ISO 14001, ISO 50001, UNE 166002 and OHSAS 18001) and experimental research based on data delivered by CDTI (Center for Industrial Technological Development) including relevant and objective information about R&D&I Projects in the energy sector. This study analyzes the impact of four variables (duration, budget, year of funding and certifications to management systems) on the success of the project. The conclusion is the significant positive impact of having management system certifications on the success of company projects analyzed in the Spanish energy sector, which may be of interest to PM practitioners in order to consider Sustainability as a factor for success.

We obtain sharp bounds for the modulus of continuity of the uncentered maximal function in terms of the modulus of continuity of the given function, via integral formulas. Some of the results deduced from these formulas are the following: The best constants for Lipschitz and Hölder functions on proper subintervals ofIn higher dimensions, we determine the asymptotic behavior, as d → ∞, of the norm of the maximal operator associated with cross-polytopes, Euclidean balls, and cubes, that is, p balls for p = 1, 2, ∞. We do this for arbitrary moduli of continuity. In the specific case of Lipschitz and Hölder functions, the operator norm of the maximal operator is uniformly bounded by 2 −α/q , where q is the conjugate exponent of p = 1, 2, and as d → ∞ the norms approach this bound. When p = ∞, best constants are the same as when p = 1.

We characterize the space BV(I ) of functions of bounded variation on an arbitrary interval I ⊂ R, in terms of a uniform boundedness condition satisfied by the local uncentered maximal operator M R from BV(I ) into the Sobolev space W 1,1 (I ). By restriction, the corresponding characterization holds for W 1,1 (I ). We also show that if U is open in R d , d > 1, then boundedness from BV(U ) into W 1,1 (U ) fails for the local directional maximal operator M v T , the local strong maximal operator M S T , and the iterated local directional maximal operator M d T • · · · • M 1 T . Nevertheless, if U satisfies a cone condition, then M S T : BV(U ) → L 1 (U ) boundedly, and the same happens with M v T , M d T • · · · • M 1 T , and M R .

Abstract. We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the ∞-norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special.