Let G be the Lie group ${\mathbb{R}}^2\rtimes {\mathbb{R}}^+$ endowed with the Riemannian symmetric space structure. Take a distinguished basis $X_0,\, X_1,\,X_2$ of left-invariant vector fields of the Lie algebra of G, and consider the Laplacian $\Delta=-\sum_{i=0}^2X_i^2$ and the first-order Riesz transforms $\mathcal R_i=X_i\Delta^{-1/2}$, $i=0,1,2$. We first show that the atomic Hardy space H1 in G introduced by the authors in a previous paper does not admit a characterization in terms of the Riesz transforms $\mathcal R_i$. It is also proved that two of these Riesz transforms are bounded from H1 to H1.

Let $v \ne 0$ be a vector in ${\mathbb {R}}^n$. Consider the Laplacian on ${\mathbb {R}}^n$ with drift $\Delta _{v} = \Delta + 2v\cdot \nabla $ and the measure $d\mu (x) = e^{2 \langle v, x \rangle } dx$, with respect to which $\Delta _{v}$ is self-adjoint. This measure has exponential growth with respect to the Euclidean distance. We study weak type $(1, 1)$ and other sharp endpoint estimates for the Riesz transforms of any order, and also for the vertical and horizontal Littlewood–Paley–Stein functions associated with the heat and the Poisson semigroups.

When a change request is raised in an engineering project an ad hoc team often forms to manage the request. Prior research shows that practitioners often view engineering changes in a risk-averse manner. As a project progresses the cost of changes increases. Therefore, avoiding changes is reasonable. However, a risk-averse perspective fails to recognize that changes might harbor discoverable and exploitable opportunities. In this research, we investigated how practitioners of ad hoc teams used practices and praxes aimed at discovering and exploiting opportunities in engineering change requests. A single case study design was employed using change request records and practitioner interviews from an engineering project. 87 engineering change requests were analyzed with regards to change triggers, time-to-decision and rejection rate. In total, 25 opportunities were discovered and then 17 exploited. Three practices and six praxes were identified, used by practitioners to discover and exploit opportunities. Our findings emphasize the importance of the informal structure of ad hoc teams, to aid in opportunity discovery. The informal structure enables cross-hierarchal discussions and draws on the proven experience of the team members. Thus, this research guides project managers and presumptive ad hoc teams in turning engineering changes into successful opportunities.

We study the heat semigroup maximal operator associated with a well-known orthonormal system in the $d$-dimensional ball. The corresponding heat kernel is shown to satisfy Gaussian bounds. As a consequence, we can prove weighted $L^{p}$ estimates, as well as some weighted inequalities in mixed norm spaces, for this maximal operator.

It is well known that the standard Lipschitz space in Euclidean space, with exponent α ∈ (0, 1), can be characterized by means of the inequality , where is the Poisson integral of the function f. There are two cases: one can either assume that the functions in the space are bounded, or one can not make such an assumption. In the setting of the Ornstein–Uhlenbeck semigroup in ℝn , Gatto and Urbina defined a Lipschitz space by means of a similar inequality for the Ornstein–Uhlenbeck Poisson integral, considering bounded functions. In a preceding paper, the authors characterized that space by means of a Lipschitz-type continuity condition. The present paper defines a Lipschitz space in the same setting in a similar way, but now without the boundedness condition. Our main result says that this space can also be described by a continuity condition. The functions in this space turn out to have at most logarithmic growth at infinity.

The Franklin spline system in [0,1] has been generalized by Strömberg to a system in ℝn which is an unconditional basis in H p (ℝn ) for p > n/(n + m +1). Here the natural number m is the order of the system. For some of these values of p, it was known that the H p quasi-norm is equivalent to a certain expression containing the coefficients of the function with respect to this basis. We prove this equivalence for all p > n/(n + m +1).

We characterize absolutely continuous and continuous measures by means of the g-function and distribution function, respectively, of the Poisson integral in a half space. Some other ways of measuring the Poisson integral are found to make such measures indistinguishable. A variant of the Poisson integral is also studied.