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1. |
Record Nr. |
UNISALENTO991002944229707536 |
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Autore |
Alvarado, Ryan |
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Titolo |
Hardy spaces on Ahlfors-regular quasi metric spaces [e-book] : a sharp theory / Ryan Alvarado, Marius Mitrea |
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Pubbl/distr/stampa |
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Cham [Switzerland] : Springer, 2015 |
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ISBN |
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Descrizione fisica |
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1 online resource (viii, 486 pages) : illustrations |
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Collana |
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Lecture notes in mathematics, 1617-9692 ; 2142 |
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Classificazione |
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AMS 42B35 |
AMS 30L05 |
AMS 35J57 |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Hardy spaces |
Quasi-metric spaces |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and indexes |
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Nota di contenuto |
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Introduction - Geometry of Quasi-Metric Spaces -- Analysis on Spaces of Homogeneous Type -- Maximal Theory of Hardy Spaces -- Atomic Theory of Hardy Spaces -- Molecular and Ionic Theory of Hardy Spaces -- Further Results -- Boundedness of Linear Operators Defined on Hp(X) -- Besov and Triebel-Lizorkin Spaces on Ahlfors-Regular Quasi-Metric Spaces |
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Sommario/riassunto |
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Systematically building an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Ahlfors-regular quasi-metric spaces. The text is broadly divided into two main parts. The first part gives atomic, molecular, and grand maximal function characterizations of Hardy spaces and formulates sharp versions of basic analytical tools for quasi-metric spaces, such as a Lebesgue differentiation theorem with minimal demands on the underlying measure, a maximally smooth approximation to the identity and a Calderon-Zygmund decomposition for distributions. These results are of independent interest. The second part establishes very general criteria guaranteeing that a linear operator acts continuously from a Hardy space into a topological vector space, emphasizing the role of the action of the operator on atoms. Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half |
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space with boundary data from Hardy spaces. The tools established in the first part are then used to develop a sharp theory of Besov and Triebel-Lizorkin spaces in Ahlfors-regular quasi-metric spaces. The monograph is largely self-contained and is intended for an audience of mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry |
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2. |
Record Nr. |
UNINA9910812502103321 |
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Autore |
Isac Daniela |
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Titolo |
I-language : an introduction to linguistics as cognitive science / / Daniela Isac and Charles Reiss |
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Pubbl/distr/stampa |
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Oxford, [England] : , : Oxford University Press, , 2008 |
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2008 |
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ISBN |
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Descrizione fisica |
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1 online resource (333 p.) |
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Collana |
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Oxford Linguistics |
Oxford Core Linguistics |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Contents; Preface; Acknowledgements; List of Figures; PART I: The Object of Inquiry; 1 What is I-language?; 1.1 Jumping in; 1.2 Equivalence classes; 1.3 Partial reduplication in Samoan; 1.4 Mentalism; 1.5 I-language; 1.6 Some implications of mentalism; 1.7 Summing up; 1.8 Exercises; 2 I-everything: Triangles, streams, words; 2.1 A triangle built by the mind; 2.2 More visual construction; 2.3 Auditory scene analysis; 2.4 Words are built by the mind; 2.5 Summing up; 2.6 Exercises; 3 Approaches to the study of language; 3.1 Commonsense views of "language"; 3.2 I-language |
3.3 The kind of stuff we look at3.4 Methodological dualism; 3.5 Biolinguistics; 3.6 And so?; 3.7 Exercises; 4 I-/E-/P-Language; 4.1 Computation in phonology; 4.2 Extensional equivalence; 4.3 Non-internalist approaches; 4.4 How is communication possible?; 4.5 |
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Exercises; PART II: Linguistic Representation and Computation; 5 A syntactic theory that won't work; 5.1 General requirements on grammars; 5.2 Finite state languages; 5.3 Discussion; 5.4 Power of grammars; 5.5 Exercises; 6 Abstract representations; 6.1 Abstractness; 6.2 Abstractness of sentence structure; 6.3 Allophony |
6.4 Turkish vowel harmony6.5 Words are not derived from words; 6.6 Think negative; 6.7 Summing up; 6.8 Exercises; 7 Some details of sentence structure; 7.1 Basic syntactic categories; 7.2 Syntactic constituents; 7.3 Labels and phrasal categories; 7.4 Predicting syntactic patterns; 7.5 Using trees to predict reaction times; 7.6 To sum up; 7.7 Exercises; 8 Binding; 8.1 Preliminaries; 8.2 Anaphors; 8.3 Pronouns and "referential expressions"; 8.4 Some implications; 8.5 Binding and wh-movement; 8.6 Non-structural factors in interpretation; 8.7 Exercises; 9 Ergativity; 9.1 Preliminaries |
9.2 A nominative-accusative system9.3 An ergative-absolutive system; 9.4 A tense-split system; 9.5 A nominal-verbal mismatch; 9.6 A NP-split system; 9.7 Language, thought and culture; 9.8 Exercises; PART III: Universal Grammar; 10 Approaches to UG: Empirical evidence; 10.1 On the plausibility of innate knowledge; 10.2 More negative thoughts; 10.3 Exercises; 11 Approaches to UG: Logic; 11.1 Let's play cards; 11.2 Where does this leave us?; 11.3 Building blocks in other domains; 11.4 Exercises; PART IV: Implications and Conclusions; 12 Social implications |
12.1 Prescriptive vs. descriptive grammar12.2 Negation; 12.3 Change is constant; 12.4 Exercises; 13 Some philosophy; 13.1 Rationalism and empiricism; 13.2 Competence and performance; 13.3 Reference; 13.4 Essentialism; 13.5 Mind and body; 13.6 A view from neuroscience; 13.7 Exercises; 14 Open questions and closing remarks; 14.1 You and your grammar; 14.2 Retracing the links among key -isms; 14.3 Bearing on philosophical questions; References; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W |
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Sommario/riassunto |
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The book introduces the major branches of theoretical linguistics - phonology, morphology, syntax, semantics - in the context of cognitive science, with reference to fields such as vision, auditory perception and philosophy of mind. - ;I-Language introduces the uninitiated to linguistics as cognitive science. In an engaging, down-to-earth style Daniela Isac and Charles Reiss give a crystal-clear demonstration of the application of the scientific method in linguistic theory. Their presentation of the research programme inspired and led by Noam Chomsky shows how the focus of theory and research |
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