Invariant potential theory in the unit ball of C n:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1994
|
| Ausgabe: | 1. publication |
| Schriftenreihe: | London Mathematical Society: London Mathematical Society Lecture Note Series
199 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006409169&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 173 Seiten |
| ISBN: | 0521468302 |
Internformat
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| 245 | 1 | 0 | |a Invariant potential theory in the unit ball of C n |c Manfred Stoll, University of South Carolina |
| 250 | |a 1. publication | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1994 | |
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Datensatz im Suchindex
| _version_ | 1819286061801537536 |
|---|---|
| adam_text | Contents
Preface
Introduction 1
1. Notation and Preliminary Results 7
1.1 Notation 7
1.2 Integral Formulas on B 10
1.3 Automorphisms of B 11
2. The Bergman Kernel 12
2.1 The Bergman Kernel 12
2.2 Examples 16
2.3 Properties of the Bergman Kernel 19
2.4 The Bergman Metric 20
3. The Laplace Beltrami Operator 23
3.1 The Invariant Laplacian 23
3.2 The Invariant Laplacian for Un 24
3.3 The Invariant Laplacian for B 25
3.4 The Invariant Gradient 27
4. Invariant Harmonic and Subharmonic Functions 31
4.1 vVl Subharmonic Functions 31
4.2 The Invariant Convolution on B 34
4.3 The Riesz Measure 36
4.4 Remarks 40
5. Poisson Szego Integrals 43
5.1 The Poisson Szego Kernel 43
5.2 The Dirichlet Problem for A 48
5.3 Poisson Szego Integrals 51
5.4 The Dirichlet Problem for rB 55
5.5 Remarks 57
6. The Riesz Decomposition Theorem 60
6.1 Harmonic Majorants for ..Vf Subharmonic Functions 61
6.2 The Green s Function for A 64
6.3 The Riesz Decomposition Theorem 67
viii Contents
6.4 Green Potentials 71
6.5 A Characterization of Hp Spaces 75
6.6 Remarks 79
7. Admissible Boundary Limits of Poisson Integrals 81
7.1 Admissible Limits of Poisson Integrals 82
7.2 Maximal Functions of Measures 83
7.3 Differentiation Theorems 87
7.4 The Admissible Maximal Function 89
7.5 Weighted Radial Limits of Poisson Integrals 92
7.6 Remarks 94
8. Radial and Admissible Boundary Limits of Potentials 96
8.1 Radial Limits of Potentials 96
8.2 Admissible Limits of Potentials 107
8.3 Tangential Limits of Potentials 114
8.4 Convergence in Lp 120
8.5 Related Results 123
9. Gradient Estimates and Riesz Potentials 126
9.1 Gradient Estimates of Green Potentials 126
9.2 Lp Inequalities for the Riesz Operator 132
10. Spaces of Invariant Harmonic Functions 142
10.1 Mean Value Inequalities for h p and Vh , 0 p oo 142
10.2 On a Theorem of Hardy and Littlewood 149
10.3 .M Harmonic Bergman and Dirichlet Spaces 152
10.4 Remarks 160
References 164
Index 171
|
| any_adam_object | 1 |
| author | Stoll, Manfred |
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| building | Verbundindex |
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| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publication |
| format | Book |
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| id | DE-604.BV009691296 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:40:37Z |
| institution | BVB |
| isbn | 0521468302 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006409169 |
| oclc_num | 243790940 |
| open_access_boolean | |
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| owner_facet | DE-12 DE-355 DE-BY-UBR DE-703 DE-29T DE-634 DE-11 DE-188 |
| physical | X, 173 Seiten |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society Lecture Note Series |
| series2 | London Mathematical Society: London Mathematical Society Lecture Note Series |
| spellingShingle | Stoll, Manfred Invariant potential theory in the unit ball of C n London Mathematical Society: London Mathematical Society Lecture Note Series Harmonische Analyse (DE-588)4023453-8 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Einheitssphäre (DE-588)4151316-2 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4169285-8 (DE-588)4151316-2 (DE-588)4046939-6 |
| title | Invariant potential theory in the unit ball of C n |
| title_auth | Invariant potential theory in the unit ball of C n |
| title_exact_search | Invariant potential theory in the unit ball of C n |
| title_full | Invariant potential theory in the unit ball of C n Manfred Stoll, University of South Carolina |
| title_fullStr | Invariant potential theory in the unit ball of C n Manfred Stoll, University of South Carolina |
| title_full_unstemmed | Invariant potential theory in the unit ball of C n Manfred Stoll, University of South Carolina |
| title_short | Invariant potential theory in the unit ball of C n |
| title_sort | invariant potential theory in the unit ball of c n |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Einheitssphäre (DE-588)4151316-2 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| topic_facet | Harmonische Analyse Mehrere komplexe Variable Einheitssphäre Potenzialtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006409169&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT stollmanfred invariantpotentialtheoryintheunitballofcn |