{"title":"Trace Operators on Regular Trees","authors":"P. Koskela, K. N. Nguyen, Zhuang Wang","doi":"10.1515/agms-2020-0117","DOIUrl":"https://doi.org/10.1515/agms-2020-0117","url":null,"abstract":"Abstract We consider different notions of boundary traces for functions in Sobolev spaces defined on regular trees and show that the almost everywhere existence of these traces is independent of the chosen definition of a trace.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"8 1","pages":"396 - 409"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0117","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48105395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Construction of Frames on the Heisenberg Groups","authors":"D. Chang, Yongsheng Han, Xinfeng Wu","doi":"10.1515/agms-2020-0118","DOIUrl":"https://doi.org/10.1515/agms-2020-0118","url":null,"abstract":"Abstract In this paper, we present a construction of frames on the Heisenberg group without using the Fourier transform. Our methods are based on the Calderón-Zygmund operator theory and Coifman’s decomposition of the identity operator on the Heisenberg group. These methods are expected to be used in further studies of several complex variables.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"8 1","pages":"382 - 395"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0118","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47928216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Real-Variable Characterizations of Hardy–Lorentz Spaces on Spaces of Homogeneous Type with Applications to Real Interpolation and Boundedness of Calderón–Zygmund Operators","authors":"Xilin Zhou, Ziyi He, Dachun Yang","doi":"10.1515/agms-2020-0109","DOIUrl":"https://doi.org/10.1515/agms-2020-0109","url":null,"abstract":"Abstract Let (𝒳, d, μ) be a space of homogeneous type, in the sense of Coifman and Weiss, with the upper dimension ω. Assume that η ∈(0, 1) is the smoothness index of the wavelets on 𝒳 constructed by Auscher and Hytönen. In this article, via grand maximal functions, the authors introduce the Hardy–Lorentz spaces H*p,q(𝒳) H_*^{p,q}left( mathcal{X} right) with the optimal range p∈(ωω+η,∞) p in left( {{omega over {omega + eta }},infty } right) and q ∈ (0, ∞]. When and p∈(ωω+η,1] p in ({omega over {omega + eta }},1] q ∈ (0, ∞], the authors establish its real-variable characterizations, respectively, in terms of radial maximal functions, non-tangential maximal functions, atoms, molecules, and various Littlewood–Paley functions. The authors also obtain its finite atomic characterization. As applications, the authors establish a real interpolation theorem on Hardy–Lorentz spaces, and also obtain the boundedness of Calderón–Zygmund operators on them including the critical cases. The novelty of this article lies in getting rid of the reverse doubling assumption of μ by fully using the geometrical properties of 𝒳 expressed via its dyadic reference points and dyadic cubes and, moreover, the results in the case q ∈ (0, 1) of this article are also new even when 𝒳 satisfies the reverse doubling condition.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"8 1","pages":"182 - 260"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0109","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49179473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ultradiversification of Diversities","authors":"Pouya Haghmaram, K. Nourouzi","doi":"10.1515/agms-2020-0100","DOIUrl":"https://doi.org/10.1515/agms-2020-0100","url":null,"abstract":"Abstract In this paper, using the idea of ultrametrization of metric spaces we introduce ultradiversification of diversities. We show that every diversity has an ultradiversification which is the greatest nonexpansive ultra-diversity image of it. We also investigate a Hausdorff-Bayod type problem in the setting of diversities, namely, determining what diversities admit a subdominant ultradiversity. This gives a description of all diversities which can be mapped onto ultradiversities by an injective nonexpansive map. The given results generalize similar results in the setting of metric spaces.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"8 1","pages":"410 - 417"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43759774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Intrinsic Characterization of Five Points in a CAT(0) Space","authors":"T. Toyoda","doi":"10.1515/agms-2020-0111","DOIUrl":"https://doi.org/10.1515/agms-2020-0111","url":null,"abstract":"Abstract Gromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"8 1","pages":"114 - 165"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0111","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49654740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ruming Gong, Ji Li, Elodie Pozzi, Manasa N. Vempati
{"title":"Commutators on Weighted Morrey Spaces on Spaces of Homogeneous Type","authors":"Ruming Gong, Ji Li, Elodie Pozzi, Manasa N. Vempati","doi":"10.1515/agms-2020-0116","DOIUrl":"https://doi.org/10.1515/agms-2020-0116","url":null,"abstract":"Abstract In this paper, we study the boundedness and compactness of the commutator of Calderón– Zygmund operators T on spaces of homogeneous type (X, d, µ) in the sense of Coifman and Weiss. More precisely, we show that the commutator [b, T] is bounded on the weighted Morrey space Lωp,k(X) L_omega ^{p,k}left( X right) with κ ∈ (0, 1) and ω ∈ Ap(X), 1 < p < ∞, if and only if b is in the BMO space. We also prove that the commutator [b, T] is compact on the same weighted Morrey space if and only if b belongs to the VMO space. We note that there is no extra assumptions on the quasimetric d and the doubling measure µ.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"8 1","pages":"305 - 334"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0116","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43158160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Admissibility versus Ap-Conditions on Regular Trees","authors":"K. N. Nguyen, Zhuang Wang","doi":"10.1515/agms-2020-0110","DOIUrl":"https://doi.org/10.1515/agms-2020-0110","url":null,"abstract":"Abstract We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"8 1","pages":"92 - 105"},"PeriodicalIF":1.0,"publicationDate":"2019-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0110","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43722350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Integral Representation of Local Left–Invariant Functionals in Carnot Groups","authors":"Alberto Maione, E. Vecchi","doi":"10.1515/agms-2020-0001","DOIUrl":"https://doi.org/10.1515/agms-2020-0001","url":null,"abstract":"Abstract The aim of this note is to prove a representation theorem for left–invariant functionals in Carnot groups. As a direct consequence, we can also provide a Г-convergence result for a smaller class of functionals.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"8 1","pages":"1 - 14"},"PeriodicalIF":1.0,"publicationDate":"2019-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45275584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Concentration of Product Spaces","authors":"Daisuke Kazukawa","doi":"10.1515/agms-2020-0129","DOIUrl":"https://doi.org/10.1515/agms-2020-0129","url":null,"abstract":"Abstract We investigate the relation between the concentration and the product of metric measure spaces. We have the natural question whether, for two concentrating sequences of metric measure spaces, the sequence of their product spaces also concentrates. A partial answer is mentioned in Gromov’s book [4]. We obtain a complete answer for this question.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"9 1","pages":"186 - 218"},"PeriodicalIF":1.0,"publicationDate":"2019-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45798753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anna Odone, Eleonora Bossi, Maddalena Gaeta, Maria Paola Garancini, Carlo Orlandi, Maria Teresa Cuppone, Carlo Signorelli, Ottavio Nicastro, Carla Maria Zotti
{"title":"Risk Management in healthcare: results from a national-level survey and scientometric analysis in Italy.","authors":"Anna Odone, Eleonora Bossi, Maddalena Gaeta, Maria Paola Garancini, Carlo Orlandi, Maria Teresa Cuppone, Carlo Signorelli, Ottavio Nicastro, Carla Maria Zotti","doi":"10.23750/abm.v90i9-S.8164","DOIUrl":"10.23750/abm.v90i9-S.8164","url":null,"abstract":"<p><p>Risk management in healthcare, intended as all processes employed to detect, monitor, assess, mitigate, and prevent risks in healthcare facilities and safeguard patient safety, is a crucial component of Italy' National Health Service. Aim of the current study is to assess the role and progress of research and training, in the field of Risk Management. We carried out a scientometric analysis to quantify and describe scientific outputs on Risk Management at the global and national level, over the last forty years; in addiction, we conducted a national-level cross-sectional survey to systematically retrieve and assess research and training activities within Italian postgraduate medical programmes in Hygiene and Preventive Medicine. We report increasing scientific production on Risk Management-related topics from 1980 to 2017 at the global level (12% annual increase rate). Clinical Trials and Systematic reviews/meta-analysis make up for respectively 5% and 6% of global scientific output. Italy ranks 4th for scientific production, after USA, UK and Germany. 88% of Italian postgraduate medical programmes in Hygiene and Preventive medicine research on Risk Management, 42% through international collaborations. The main research themes are Healthcare-Associated Infections (HAIs) (97%), analysis of organizational models for safety in healthcare (62%), while training is focused on internships (87%) and academic lectures (73%). While research provides the evidence required to plan, implement and monitor effective interventions in healthcare risk management, training allows its dissemination in a synergic action to promote the value of patient safety and quality of care.</p>","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"10 1","pages":"76-86"},"PeriodicalIF":0.0,"publicationDate":"2019-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7233657/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68833136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}