Nonlinear superposition operators:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Pr.
1990
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
95 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 311 S. |
| ISBN: | 0521361028 |
Staff View
MARC
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| 100 | 1 | |a Appell, Jürgen |d 1952- |e Verfasser |0 (DE-588)140990860 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear superposition operators |c Jürgen Appell ; Petr P. Zabrejko |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1990 | |
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| 700 | 1 | |a Zabrejko, Petr Petrovič |d 1939- |e Verfasser |0 (DE-588)110493575 |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface 1
Chapter 1 7
The superposition operator in the space S
1.1 The space S 7
1.2 The superposition operator 10
1.3 Sup-measurable functions 12
1.4 Caratheodory and Shragin functions 16
1.5 Boundedness conditions 19
1.6 Continuity conditions 22
1.7 Compactness conditions 28
1.8 Special classes of functions 30
1.9 Notes, remarks and references 33
Chapter 2 39
The superposition operator in ideal spaces
2.1 Ideal spaces 40
2.2 The domain of definition of the superposition operator 44
2.3 Local and global boundedness conditions 48
2.4 Special boundedness properties 54
2.5 Continuity conditions 58
2.6 Lipschitz and Darbo conditions 64
2.7 Differentiability conditions 70
2.8 Higher derivatives and analyticity 75
2.9 Notes, remarks and references 82
Chapter 3 89
The superposition operator in Lebesgue spaces
3.1 Lebesgue spaces 90
3.2 Acting conditions 93
3.3 The growth function 96
3.4 Absolute boundedness and uniform continuity 100
3.5 Lipschitz and Darbo conditions 103
3.6 Differentiability conditions and analyticity 107
3.7 The case p = oo or g = oo 110
3.8 The ^-characteristic 111
3.9 Notes, remarks and references 114
Chapter 4 119
The superposition operator in Orlicz spaces
4.1 Orlicz spaces 119
4.2 Acting conditions 125
4.3 Boundedness conditions 128
4.4 Continuity conditions 130
4.5 Lipschitz and Darbo conditions 131
4.6 Differentiability conditions and analyticity 134
4.7 Notes, remarks and references 136
Chapter 5 141
The superposition operator in symmetric spaces
5.1 Symmetric spaces 141
5.2 Lorentz and Marcinkiewicz spaces 150
5.3 Acting conditions in symmetric spaces 155
5.4 Some properties in symmetric spaces 157
5.5 Notes, remarks and references 159
Chapter 6 163
The superposition operator in the spaces C and BV
6.1 The space C 163
6.2 Some properties of Caratheodory functions 165
6.3 The superposition operator in the space C 167
6.4 The superposition operator between C and S 171
6.5 The superposition operator in the space BV 172
6.6 Notes, remarks and references 177
Chapter 7 181
The superposition operator in Holder spaces
7.1 Holder spaces 182
7.2 Acting conditions 184
7.3 Boundedness conditions 188
7.4 Continuity conditions 191
7.5 Lipschitz and Darbo conditions 194
7.6 Differentiability conditions 197
7.7 The superposition operator in the space J$p 198
7.8 Notes, remarks and references 200
Chapter 8 205
The superposition operator in spaces of smooth functions
8.1 The spaces Ck and H* 205
8.2 The superposition operator in the space Ck 207
8.3 The superposition operator in the space H% 215
8.4 The superposition operator in the space R^(L) 217
8.5 The superposition operator in Roumieu classes 222
8.6 Notes, remarks and references 224
Chapter 9 227
The superposition operator in Sobolev spaces
9.1 Sobolev spaces 227
9.2 Sufficient acting conditions in W^ 230
9.3 Necessary acting conditions in W^ 234
9.4 Boundedness and continuity conditions in W^ 239
9.5 Boundedness and continuity conditions in W* 243
9.6 Degeneracy results 248
9.7 The superposition operator in Sobolev-Orlicz spaces 250
9.8 Notes, remarks and references 253
Bibliography 259
List of Symbols 297
Subject Index 303
|
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| id | DE-604.BV003710521 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:04:13Z |
| institution | BVB |
| isbn | 0521361028 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002361998 |
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| physical | 311 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Appell, Jürgen 1952- Verfasser (DE-588)140990860 aut Nonlinear superposition operators Jürgen Appell ; Petr P. Zabrejko 1. publ. Cambridge u.a. Cambridge Univ. Pr. 1990 311 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 95 Nichtlinearer Operator (DE-588)4225824-8 gnd rswk-swf Superpositionsoperator (DE-588)4184122-0 gnd rswk-swf Superpositionsoperator (DE-588)4184122-0 s DE-604 Nichtlinearer Operator (DE-588)4225824-8 s Zabrejko, Petr Petrovič 1939- Verfasser (DE-588)110493575 aut Cambridge tracts in mathematics 95 (DE-604)BV000000001 95 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002361998&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Appell, Jürgen 1952- Zabrejko, Petr Petrovič 1939- Nonlinear superposition operators Cambridge tracts in mathematics Nichtlinearer Operator (DE-588)4225824-8 gnd Superpositionsoperator (DE-588)4184122-0 gnd |
| subject_GND | (DE-588)4225824-8 (DE-588)4184122-0 |
| title | Nonlinear superposition operators |
| title_auth | Nonlinear superposition operators |
| title_exact_search | Nonlinear superposition operators |
| title_full | Nonlinear superposition operators Jürgen Appell ; Petr P. Zabrejko |
| title_fullStr | Nonlinear superposition operators Jürgen Appell ; Petr P. Zabrejko |
| title_full_unstemmed | Nonlinear superposition operators Jürgen Appell ; Petr P. Zabrejko |
| title_short | Nonlinear superposition operators |
| title_sort | nonlinear superposition operators |
| topic | Nichtlinearer Operator (DE-588)4225824-8 gnd Superpositionsoperator (DE-588)4184122-0 gnd |
| topic_facet | Nichtlinearer Operator Superpositionsoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002361998&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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