Coverart for item
The Resource Analysis in Banach Spaces, Volume I, Martingales and Littlewood-Paley theory, by Tuomas Hytönen, Jan van Neerven, Mark Veraar and Lutz Weis, (electronic book)

Analysis in Banach Spaces, Volume I, Martingales and Littlewood-Paley theory, by Tuomas Hytönen, Jan van Neerven, Mark Veraar and Lutz Weis, (electronic book)

Label
Analysis in Banach Spaces, Volume I, Martingales and Littlewood-Paley theory
Title
Analysis in Banach Spaces
Title number
Volume I
Title part
Martingales and Littlewood-Paley theory
Statement of responsibility
by Tuomas Hytönen, Jan van Neerven, Mark Veraar and Lutz Weis
Title variation
Martingales and Littlewood-Paley theory
Creator
Contributor
Author
Subject
Language
eng
Summary
The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas
Member of
Cataloging source
EBLCP
http://library.link/vocab/creatorName
Hytönen, Tuomas
Dewey number
  • 515/.732
  • 510
Index
no index present
LC call number
  • QA322.2
  • QA1-939
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • van Neerven, Jan, 1964-
  • Veraar, Mark C.
  • Weis, Lutz
Series statement
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series volume
v. 63
http://library.link/vocab/subjectName
  • Banach spaces
  • Fourier Analysis
Label
Analysis in Banach Spaces, Volume I, Martingales and Littlewood-Paley theory, by Tuomas Hytönen, Jan van Neerven, Mark Veraar and Lutz Weis, (electronic book)
Instantiates
Publication
Note
4.3.a Reflexivity
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; Symbols and notations; Standing assumptions; 1 Bochner spaces; 1.1 Measurability; 1.1.a Functions on a measurable space (S; A); 1.1.b Functions on a measure space (S; A ;); 1.1.c Operator-valued functions; 1.2 Integration; 1.2.a The Bochner integral; 1.2.c The Pettis integral; 1.3 Duality of Bochner spaces; 1.3.a Elementary duality results; 1.3.b Duality and the Radon-Nikodým property; 1.3.c More about the Radon-Nikodým property; 1.4 Notes; 2 Operators on Bochner spaces; 2.1 The Lp-extension problem ; 2.1.a Boundedness of T IX for positive operators T
  • 2.1.b Boundedness of T IH for Hilbert spaces H2.1.c Counterexamples; 2.2 Interpolation of Bochner spaces; 2.2.a The Riesz-Thorin interpolation theorem; 2.2.b The Marcinkiewicz interpolation theorem; 2.2.c Complex interpolation of the spaces Lp(S; X); 2.2.d Real interpolation of the spaces Lp(S; X); 2.3 The Hardy-Littlewood maximal operator; 2.3.a Lebesgue points and differentiation; 2.3.b Convolutions and approximation; 2.4 The Fourier transform; 2.4.a The inversion formula and Plancherel's theorem; 2.4.b Fourier type; 2.4.c The Schwartz class S(Rd; X)
  • 2.4.d The space of tempered distributions S0(RdX); 2.5 Sobolev spaces and differentiability; 2.5.a Weak derivatives; 2.5.b The Sobolev spaces Wk; p(D; X); 2.5.c Almost everywhere differentiability; 2.5.d The fractional Sobolev spaces Ws; p(Rd; X); 2.6 Conditional expectations; 2.6.a Uniqueness; 2.6.b Existence; 2.6.c Conditional limit theorems; 2.6.d Inequalities and identities; 2.7 Notes; 3 Martingales; 3.1 Definitions and basic properties; 3.1.a Difference sequences; 3.1.b Paley-Walsh martingales; 3.1.c Stopped martingales; 3.2 Martingale inequalities; 3.2.a Doob's maximal inequalities
  • 3.2.b Rademacher variables and contraction principles3.2.c John-Nirenberg and Kahane-Khintchine inequalities; 3.2.d Applications to inequalities on; 3.3 Martingale convergence; 3.3.a Forward convergence; 3.3.b Backward convergence; 3.3.c The Itô-Nisio theorem for martingales; 3.3.d Martingale convergence and the RNP; 3.4 Martingale decompositions; 3.4.a Gundy decomposition; 3.4.b Davis decomposition; 3.5 Martingale transforms; 3.5.a Basic properties; 3.5.b Extrapolation of Lp-inequalities; 3.5.c End-point estimates in L1 ; 3.5.d Martingale type and cotype
  • 3.6 Approximate models for martingales3.6.a Universality of Paley-Walsh martingales; 3.6.b The Rademacher maximal function; 3.6.c Approximate models for martingale transforms; 3.7 Notes; 4 UMD spaces; 4.1 Motivation; 4.1.a Square functions for martingale difference sequences; 4.1.b Unconditionality; 4.2 The UMD property; 4.2.a Definition and basic properties; 4.2.b Unconditionality of the Haar decomposition; 4.2.c Examples and constructions; 4.2.d Stein's inequality for conditional expectations; 4.2.e Boundedness of martingale transforms; 4.3 Banach space properties implied by UMD
Dimensions
unknown
Extent
1 online resource (628 pages).
Form of item
online
Isbn
9783319485195
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-48520-1
Specific material designation
remote
System control number
  • SPR965164867
  • ocn965164867
Label
Analysis in Banach Spaces, Volume I, Martingales and Littlewood-Paley theory, by Tuomas Hytönen, Jan van Neerven, Mark Veraar and Lutz Weis, (electronic book)
Publication
Note
4.3.a Reflexivity
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; Symbols and notations; Standing assumptions; 1 Bochner spaces; 1.1 Measurability; 1.1.a Functions on a measurable space (S; A); 1.1.b Functions on a measure space (S; A ;); 1.1.c Operator-valued functions; 1.2 Integration; 1.2.a The Bochner integral; 1.2.c The Pettis integral; 1.3 Duality of Bochner spaces; 1.3.a Elementary duality results; 1.3.b Duality and the Radon-Nikodým property; 1.3.c More about the Radon-Nikodým property; 1.4 Notes; 2 Operators on Bochner spaces; 2.1 The Lp-extension problem ; 2.1.a Boundedness of T IX for positive operators T
  • 2.1.b Boundedness of T IH for Hilbert spaces H2.1.c Counterexamples; 2.2 Interpolation of Bochner spaces; 2.2.a The Riesz-Thorin interpolation theorem; 2.2.b The Marcinkiewicz interpolation theorem; 2.2.c Complex interpolation of the spaces Lp(S; X); 2.2.d Real interpolation of the spaces Lp(S; X); 2.3 The Hardy-Littlewood maximal operator; 2.3.a Lebesgue points and differentiation; 2.3.b Convolutions and approximation; 2.4 The Fourier transform; 2.4.a The inversion formula and Plancherel's theorem; 2.4.b Fourier type; 2.4.c The Schwartz class S(Rd; X)
  • 2.4.d The space of tempered distributions S0(RdX); 2.5 Sobolev spaces and differentiability; 2.5.a Weak derivatives; 2.5.b The Sobolev spaces Wk; p(D; X); 2.5.c Almost everywhere differentiability; 2.5.d The fractional Sobolev spaces Ws; p(Rd; X); 2.6 Conditional expectations; 2.6.a Uniqueness; 2.6.b Existence; 2.6.c Conditional limit theorems; 2.6.d Inequalities and identities; 2.7 Notes; 3 Martingales; 3.1 Definitions and basic properties; 3.1.a Difference sequences; 3.1.b Paley-Walsh martingales; 3.1.c Stopped martingales; 3.2 Martingale inequalities; 3.2.a Doob's maximal inequalities
  • 3.2.b Rademacher variables and contraction principles3.2.c John-Nirenberg and Kahane-Khintchine inequalities; 3.2.d Applications to inequalities on; 3.3 Martingale convergence; 3.3.a Forward convergence; 3.3.b Backward convergence; 3.3.c The Itô-Nisio theorem for martingales; 3.3.d Martingale convergence and the RNP; 3.4 Martingale decompositions; 3.4.a Gundy decomposition; 3.4.b Davis decomposition; 3.5 Martingale transforms; 3.5.a Basic properties; 3.5.b Extrapolation of Lp-inequalities; 3.5.c End-point estimates in L1 ; 3.5.d Martingale type and cotype
  • 3.6 Approximate models for martingales3.6.a Universality of Paley-Walsh martingales; 3.6.b The Rademacher maximal function; 3.6.c Approximate models for martingale transforms; 3.7 Notes; 4 UMD spaces; 4.1 Motivation; 4.1.a Square functions for martingale difference sequences; 4.1.b Unconditionality; 4.2 The UMD property; 4.2.a Definition and basic properties; 4.2.b Unconditionality of the Haar decomposition; 4.2.c Examples and constructions; 4.2.d Stein's inequality for conditional expectations; 4.2.e Boundedness of martingale transforms; 4.3 Banach space properties implied by UMD
Dimensions
unknown
Extent
1 online resource (628 pages).
Form of item
online
Isbn
9783319485195
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-48520-1
Specific material designation
remote
System control number
  • SPR965164867
  • ocn965164867

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