Function spaces. Volume 1 / Luboš Pick [and others].
Material type:
TextSeries: De Gruyter series in nonlinear analysis and applications ; 14.Publication details: Berlin : De Gruyter, 2013.Edition: 2nd rev. and extended edDescription: 1 online resource (xv, 479 pages) : illustrationsContent type: - text
- computer
- online resource
- 9783110250428
- 311025042X
- 3110250411
- 9783110250411
- 515.73
- QA323
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OPJGU Sonepat- Campus | E-Books EBSCO | Available |
Includes bibliographical references and index.
Preface; 1 Preliminaries; 1.1 Vector space; 1.2 Topological spaces; 1.3 Metric, metric space; 1.4 Norm, normed linear space; 1.5 Modular spaces; 1.6 Inner product, inner product space; 1.7 Convergence, Cauchy sequences; 1.8 Density, separability; 1.9 Completeness; 1.10 Subspaces; 1.11 Products of spaces; 1.12 Schauder bases; 1.13 Compactness; 1.14 Operators (mappings); 1.15 Isomorphism, embeddings; 1.16 Continuous linear functionals; 1.17 Dual space, weak convergence; 1.18 The principle of uniform boundedness; 1.19 Reflexivity; 1.20 Measure spaces: general extension theory.
1.21 The Lebesgue measure and integral1.22 Modes of convergence; 1.23 Systems of seminorms, Hahn-Saks theorem; 2 Spaces of smooth functions; 2.1 Multiindices and derivatives; 2.2 Classes of continuous and smooth functions; 2.3 Completeness; 2.4 Separability, bases; 2.5 Compactness; 2.6 Continuous linear functionals; 2.7 Extension of functions; 3 Lebesgue spaces; 3.1 Lp-classes; 3.2 Lebesgue spaces; 3.3 Mean continuity; 3.4 Mollifiers; 3.5 Density of smooth functions; 3.6 Separability; 3.7 Completeness; 3.8 The dual space; 3.9 Reflexivity; 3.10 The space L8; 3.11 Hardy inequalities.
6.4 Reflexivity of Banach function spaces6.5 Separability in Banach function spaces; 7 Rearrangement-invariant spaces; 7.1 Nonincreasing rearrangements; 7.2 Hardy-Littlewood inequality; 7.3 Resonant measure spaces; 7.4 Maximal nonincreasing rearrangement; 7.5 Hardy lemma; 7.6 Rearrangement-invariant spaces; 7.7 Hardy-Littlewood-Pólya principle; 7.8 Luxemburg representation theorem; 7.9 Fundamental function; 7.10 Endpoint spaces; 7.11 Almost-compact embeddings; 7.12 Gould space; 8 Lorentz spaces; 8.1 Definition and basic properties; 8.2 Embeddings between Lorentz spaces.
This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces to study other topics such as partial differential equations. Volume 1 deals with Banach function spaces, Volume 2 with Sobolev-type spaces.
English.
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