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Function Spaces, 1 Volume 1

:	Lubo? Pick, Alois Kufner, Oldrich John, Svatopluk Fucík
:	Function Spaces, 1 Volume 1
:	Walter de Gruyter GmbH& Co.KG
:	9783110250428
:	De Gruyter Series in Nonlinear Analysis and ApplicationsISSN
:	1
:	CHF 205.10
:

:	Allgemeines, Lexika
:	English

:	494
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

< >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.

< TRONG>Lubo? Pick, Charles University, Prague, Czech Republic;Alois Kufner, The Academy of Sciences of the Czech Republic, Prague, Czech Republic;Old?ich John, Charles University, Prague, Czech Republic;Svatopluk Fu?ík?.

	Preface	5
	1 Preliminaries	17
	1.1 Vector space	17
	1.2 Topological spaces	18
	1.3 Metric, metric space	22
	1.4 Norm, normed linear space	22
	1.5 Modular spaces	23
	1.6 Inner product, inner product space	26
	1.7 Convergence, Cauchy sequences	27
	1.8 Density, separability	28
	1.9 Completeness	28
	1.10 Subspaces	29
	1.11 Products of spaces	30
	1.12 Schauder bases	30
	1.13 Compactness	31
	1.14 Operators (mappings)	32
	1.15 Isomorphism, embeddings	34
	1.16 Continuous linear functionals	35
	1.17 Dual space, weak convergence	36
	1.18 The principle of uniform boundedness	37
	1.19 Reflexivity	37
	1.20 Measure spaces: general extension theory	38
	1.21 The Lebesgue measure and integral	45
	1.22 Modes of convergence	50
	1.23 Systems of seminorms, Hahn-Saks theorem	52
	2 Spaces of smooth functions	54
	2.1 Multiindices and derivatives	54
	2.2 Classes of continuous and smooth functions	55
	2.3 Completeness	59
	2.4 Separability, bases	61
	2.5 Compactness	67
	2.6 Continuous linear functionals	71
	2.7 Extension of functions	75
	3 Lebesgue spaces	78
	3.1 Lp-classes	78
	3.2 Lebesgue spaces	82
	3.3 Mean continuity	83
	3.4 Mollifiers	85
	3.5 Density of smooth functions	87
	3.6 Separability	87
	3.7 Completeness	88
	3.8 The dual space	90
	3.9 Reflexivity	94
	3.10 The space L8	94
	3.11 Hardy inequalities	99
	3.12 Sequence spaces	108
	3.13 Modes of convergence	109
	3.14 Compact subsets	110
	3.15 Weak convergence	111
	3.16 Isomorphism of Lp(O) and Lp(0, µ(O))	112
	3.17 Schauder bases	113
	3.18 Weak Lebesgue spaces	117
	3.19 Remarks	120
	4 Orlicz spaces	124
	4.1 Introduction	124
	4.2 Young function, Jensen inequality	125
	4.3 Complementary functions	131
	4.4 The .2-condition	135
	4.5 Comparison of Orlicz classes	138
	4.6 Orlicz spaces	142
	4.7 Hölder inequality in Orlicz spaces	147
	4.8 The Luxemburg norm	150
	4.9 Completeness of Orlicz spaces	153
	4.10 Convergence in Orlicz spaces	154
	4.11 Separability	159
	4.12 The space EF(O)	161
	4.13 Continuous linear functionals	167
	4.14 Compact subsets of Orlicz spaces	171
	4.15 Further properties of Orlicz spaces	177
	4.16 Isomorphism properties, Schauder bases	179
	4.17 Comparison of Orlicz spaces	182
	5 Morrey and Campanato spaces	189
	5.1 Introduction	189
	5.2 Marcinkiewicz spaces	189
	5.3 Morrey and Campanato spaces	192
	5.4 Completeness