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In this paper we establish inclusions and noninclusions between various Hardy type spaces on noncompact Riemannian manifolds M with Ricci curvature bounded from below, positive injectivity radius and spectral gap. Our first main result states that, if L is the positive Laplace–Beltrami operator on M, then the Riesz–Hardy space HR1(M) is the isomorphic image of the Goldberg type space h1(M) via the map L1/2(I+L)−1/2, a fact that is false in Rn. Specifically, HR1(M) agrees with the Hardy type space X1/2(M) recently introduced by the first three authors; as a consequence, we prove that HR1(M) does not admit an atomic characterisation. Noninclusions are mostly proved in the special case where the manifold is a Damek–Ricci space S. Our second main result states that HR1(S), the heat Hardy space HH1(S) and the Poisson–Hardy space HP1(S) are mutually distinct spaces, a fact which is in sharp contrast to the Euclidean case, where these three spaces agree.

We establish sharp-in-time kernel and dispersive estimates for the Schrödinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties are more pronounced in large time and enable us to prove the global-in-time Strichartz inequality for a larger family of admissible couples than in the Euclidean case. Consequently, we obtain the global well-posedness for the corresponding semilinear equation with lower regularity data and some scattering properties for small powers which are known to fail in the Euclidean setting. The crucial kernel estimates are achieved by combining the stationary phase method based on a subtle barycentric decomposition, a subordination formula of the Schrödinger group to the wave propagator and an improved Hadamard parametrix.

We prove a radial maximal function characterisation of the local atomic Hardy space h1(M) on a Riemannian manifold M with positive injectivity radius and Ricci curvature bounded from below. As a consequence, we show that an integrable function belongs to h1(M) if and only if either its local heat maximal function or its local Poisson maximal function is integrable. A key ingredient is a decomposition of Hölder cut-offs in terms of an appropriate class of approximations of the identity, which we obtain on arbitrary Ahlfors-regular metric measure spaces and generalises a previous result of A. Uchiyama.

Several research contributions have depicted the impact of the pandemic environment on healthcare and social care personnel. Even though the high prevalence of burnout depression and anxiety in healthcare settings before COVID-19 has been well documented in the research, the recent increase in psychological distress and mental health issues in healthcare and mental health workers should be attributed to the effect of the COVID-19 pandemic. The aim of the present study is to develop, evaluate, and compare a model of COVID-19 workplace stressors between two different territories, the Italian region of Lombardy and the Canadian province of Quebec. Within this model, burnout is depicted as the strongest determinant of mental health symptoms for mental health workers. In turn, the main workplace determinants of burnout are the perception of a lack of support from the organization and the fear of contracting COVID-19 at work. Findings also provide insights for designing interventions to promote and protect mental health workers in the context of the pandemic. In conclusion, it is necessary to monitor burnout and carefully analyze elements of organizational culture, in addition to offering clinical and psychological care for those in need. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

No instrument has been developed to explicitly assess the professional culture of mental health workers interacting with severely mentally ill people in publicly or privately run mental health care services. Because of theoretical and methodological concerns, we designed a self-administered questionnaire to assess the professional culture of mental health services workers. The study aims to validate this tool, named the Mental Health Professional Culture Inventory (MHPCI). The MHPCI adopts the notion of 'professional culture' as a hybrid construct between the individual and the organisational level that could be directly associated with the professional practices of mental health workers.Methods The MHPCI takes into consideration a multidimensional definition of professional culture and a discrete number of psychometrically derived dimensions related to meaningful professional behaviour. The questionnaire was created and developed by a conjoint Italian-Canadian research team with the purpose of obtaining a fully cross-cultural questionnaire and was pretested in a pilot study. Subsequently, a validation survey was conducted in northern Italy and in Canada (Montreal area, Quebec). Data analysis was conducted in different steps designed to maximise the cross-cultural adaptation of the questionnaire through a recursive procedure consisting of performing a principal component analysis (PCA) on the Italian sample (N = 221) and then testing the resulting factorial model on the Canadian sample (N = 237). Reliability was also assessed with a test-retest design.Results Four dimensions emerged in the PCA and were verified in the confirmatory factor analysis: family involvement, users' sexuality, therapeutic framework and management of aggression risk. All the scales displayed good internal consistency and reliability.Conclusions This study suggests the MHPCI could be a valid and reliable instrument to measure the professional behaviour of mental health services workers. The co

In this note we prove various sharp boundedness results on suitable Hardy type spaces for Riesz transforms of arbitrary order on noncompact symmetric spaces of arbitrary rank

In this paper we consider a complete connected noncompact Rieman- nian manifold M with bounded geometry and spectral gap. We realize the dual space Yk(M) of the Hardy- Type space Xk(M), introduced in a previous paper of the authors, as the class of all locally square integrable functions satisfying suitable BMO-like conditions, where the role of the constants is played by the space of global fc-quasi-harmonic functions. Furthermore we prove that Yk(M) is also the dual of the space Xn(M) of finite linear combination of Xk- Atoms. As a consequence, if Z is a Banach space and T is a Z-valued linear operator defined on then T extends to a bounded operator from Xk(M) to Z if and only if it is uniformly bounded on xk - Atoms. To obtain these results we prove the global solvability of the generalized Poisson equation&ku = / with / e L2.ioc (M) and we study some properties of generalized Bergman spaces of harmonic functions on geodesic balls.

In this paper we prove boundedness results on atomic Hardy type spaces for multipliers of the spherical transform on noncompact symmetric spaces of arbitrary rank. The multipliers we consider satisfy either inhomogeneous or homogeneous Mihlin-Hörmander type conditions. In particular, we are able to treat the case of strongly singular multipliers whose convolution kernels are not integrable at infinity. Thus our results apply also to negative and imaginary powers of the Laplacian.

Aim. The Functioning Assessment Short Test (FAST) is a useful instrument for the assessment of overall functioning of people with bipolar disorder, showing good psychometric properties. The aim of this study is to validate the Italian version of FAST. Methods. Translation and back-translation of the original FAST Spanish version were performed. Participants with bipolar disorder (n = 132) and healthy controls (n = 132) completed the FAST as a part of an assessment package including the Montgomery-Asberg Depression Rating Scale and the Young Mania Rating Scale. Internal consistency, inter-rater reliability, construct and discriminant validity were assessed. Results. The FAST Italian version showed good internal consistency, inter-rater reliability and discriminant validity. The cut-off discriminating patients from controls was 15, with a sensitivity of 0.79 and a specificity of 0.80. Principal component analysis with oblique rotation showed factor loadings consistent with the a priori structure of the instrument. Conclusions. This study confirmed the psychometric properties of FAST and extended its generalization and validity to the Italian population.

In this paper we consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the Hardy type spaces X k(M), introduced in a previous paper of the authors, have an atomic characterization. An atom in X k(M) is an atom in the Hardy space H 1(M) introduced by Carbonaro, Mauceri, and Meda, satisfying an "infinite dimensional" cancellation condition. As an application, we prove that the Riesz transforms of even order 2kL-k map X k(M) into L 1(T 2kM). © Mathematica Josephina, Inc. 2011.

Background: Several guidelines consider psychosocial treatments an essential component of clinical management of bipolar disorders in addition to drug therapy. However, to what extent such interventions are available in everyday practice to the average patient attending mental health services is not known. Aims: This study aims to investigate access of people with bipolar disorders to psychosocial treatments in a community-based care system. Method: Information on care delivery and service utilization were retrieved from the psychiatric database of Lombardy, Italy, covering a population of 9,743,000, for all adults who had at least one contact in 2009 with psychiatric services. Rates of patients with a diagnosis of bipolar disorder who had access to individual psychotherapy, couple/family therapy, group psychotherapy and family interventions were calculated and compared to patients with schizophrenia and depression. Results: A total of 8,899 subjects with bipolar disorder had been in contact with psychiatric services, corresponding to a treated annual prevalence rate of 1.1‰. More than 80% of patients were treated in community settings. Rates of patients receiving structured psychosocial treatments ranged from 0.7% for couple/family therapy to 6.1% for individual psychotherapy. No differences with patients with schizophrenia and depression were found. Patients with schizophrenia received more interventions labeled as rehabilitation. Conclusion: Few people with bipolar disorders had access to psychosocial treatments. Even in a well-developed system of community care, offer of psychosocial interventions for bipolar disorders is inadequate. This issue should be a target for future research on dissemination and implementation strategies.

We consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the imaginary powers of the Laplacian and the Riesz transform are bounded from the Hardy space X1(M), introduced in previous work of the authors, to L1(M).