Operator Valued Hardy Spaces
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Operator Valued Hardy Spaces
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Author : Tao Mei
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Operator Valued Hardy Spaces written by Tao Mei and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of noncommutative martingale inequalities. in this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it isproved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: (i) The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H 1$ and $\mathrm{BMO $. (ii) The atomic decomposition of theauthor's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1
Operator Valued Hardy Spaces
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Author : Tao Mei
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Operator Valued Hardy Spaces written by Tao Mei and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of noncommutative martingale inequalities. In this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it is proved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: (i) The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H 1$ and $\mathrm{BMO $. (ii) The atomic decomposition of the author's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1 \infty )$. (iv) The noncommutative Hardy-Littlewood maximal inequality. (v) A description of BMO as an intersection of two dyadic BMO. (vi) The interpolation results on these Hardy spaces.
Hardy Classes And Operator Theory
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Author : Marvin Rosenblum
language : en
Publisher: Courier Corporation
Release Date : 1997-01-01
Hardy Classes And Operator Theory written by Marvin Rosenblum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
Concise treatment focuses on theory of shift operators, Toeplitz operators and Hardy classes of vector- and operator-valued functions. Topics include general theory of shift operators on a Hilbert space, use of lifting theorem to give a unified treatment of interpolation theorems of the Pick-Nevanlinna and Loewner types, more. Appendix. Bibliography. 1985 edition.
Dirichlet Series And Holomorphic Functions In High Dimensions
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Author : Andreas Defant
language : en
Publisher: Cambridge University Press
Release Date : 2019-08-08
Dirichlet Series And Holomorphic Functions In High Dimensions written by Andreas Defant and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-08 with Mathematics categories.
Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.
Hardy Spaces And Potential Theory On C 1 Domains In Riemannian Manifolds
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Author : Martin Dindoš
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Hardy Spaces And Potential Theory On C 1 Domains In Riemannian Manifolds written by Martin Dindoš and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The author studies Hardy spaces on C1 and Lipschitz domains in Riemannian manifolds. Hardy spaces, originally introduced in 1920 in complex analysis setting, are invaluable tool in harmonic analysis. For this reason these spaces have been studied extensively by many authors.
Sobolev Besov And Triebel Lizorkin Spaces On Quantum Tori
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Author : Xiao Xiong
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-03-19
Sobolev Besov And Triebel Lizorkin Spaces On Quantum Tori written by Xiao Xiong and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.
This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative -torus (with a skew symmetric real -matrix). These spaces share many properties with their classical counterparts. The authors prove, among other basic properties, the lifting theorem for all these spaces and a Poincaré type inequality for Sobolev spaces.
Operator Valued Hardy Spaces And Related Subjects
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Author : Tao Mei
language : en
Publisher:
Release Date : 2006
Operator Valued Hardy Spaces And Related Subjects written by Tao Mei and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
We give a systematic study of the Hardy spaces of functions with values in the non-commutative Lp-spaces associated with a semifinite von Neumann algebra M. This is motivated by matrix valued harmonic analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of non-commutative martingale inequalities. Our non-commutative Hardy spaces are defined by non-commutative Lusin integral functions. It is proved in this dissertation that they are equivalent to those defined by the non-commutative Littlewood-Paley G-functions. We also study the Lp boundedness of operator valued dyadic paraproducts and prove that their Lq boundedness implies their Lp boundedness for all 1
Function Spaces In Analysis
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Author : Krzysztof Jarosz
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-07-28
Function Spaces In Analysis written by Krzysztof Jarosz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-28 with Education categories.
This volume contains the proceedings of the Seventh Conference on Function Spaces, which was held from May 20-24, 2014 at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.
Operator Theory In Function Spaces
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Author : Kehe Zhu
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Operator Theory In Function Spaces written by Kehe Zhu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
Recent Advances In Operator Theory
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Author : A. Dijksma
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Recent Advances In Operator Theory written by A. Dijksma and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains a selection of papers in modern operator theory and its applications. Most of them are directly related to lectures presented at the Inter national Workshop on Operator Theory and its Applications held at the University of Groningen (IWOTA-98) in Groningen, the Netherlands, from June 30-July 3, 1998. The workshop was attended by 97 mathematicians-of which 12 were PhD or postdoctoral students-from 19 countries. The program consisted of 19 plenary lectures of 40 minutes and 72 lectures of 30 minutes in 4 parallell sessions. The present volume reflects the wide range and rich variety of topics presented and discussed at the workshop. The papers deal with operator polynomials and analytic operator functions, with spectral problems of (partial) differential oper ators and related operator matrices, with interpolation, completion and extension problems, with commutant lifting and dilation, with Ricatti equations and real ization problems, with scattering theory, with problems from harmonic analysis, and with topics in the theory of reproducing kernel spaces and of spaces with an indefinite metric. All papers underwent the usual refereeing process.