Harmonic measure: geometric and analytic points of view
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2005]
|
| Series: | University lecture series
Volume 35 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 155 Seiten Diagramme |
| ISBN: | 0821827286 9780821827284 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV020836150 | ||
| 003 | DE-604 | ||
| 005 | 20230821 | ||
| 007 | t | ||
| 008 | 051019s2005 |||| |||| 00||| eng d | ||
| 020 | |a 0821827286 |9 0-8218-2728-6 | ||
| 020 | |a 9780821827284 |9 978-0-8218-2728-4 | ||
| 035 | |a (OCoLC)440975405 | ||
| 035 | |a (DE-599)BVBBV020836150 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-91G |a DE-83 |a DE-739 |a DE-11 |a DE-188 |a DE-824 | ||
| 080 | |a 517.9 | ||
| 084 | |a SK 560 |0 (DE-625)143246: |2 rvk | ||
| 084 | |a SI 165 |0 (DE-625)143085: |2 rvk | ||
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a MAT 310f |2 stub | ||
| 084 | |a 28A75 |2 msc | ||
| 084 | |a MAT 350f |2 stub | ||
| 084 | |a 31C05 |2 msc | ||
| 100 | 1 | |a Capogna, Luca |d 1966- |e Verfasser |0 (DE-588)132920174 |4 aut | |
| 245 | 1 | 0 | |a Harmonic measure |b geometric and analytic points of view |c Luca Capogna ; Carlos E. Kenig ; Loredana Lanzani |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2005] | |
| 264 | 4 | |c © 2005 | |
| 300 | |a x, 155 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a University lecture series |v Volume 35 | |
| 650 | 0 | 7 | |a Harmonisches Maß |0 (DE-588)4159134-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonisches Maß |0 (DE-588)4159134-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kenig, Carlos E. |d 1953- |e Verfasser |0 (DE-588)137012624 |4 aut | |
| 700 | 1 | |a Lanzani, Loredana |d 1965- |e Verfasser |0 (DE-588)173787754 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-2180-9 |
| 830 | 0 | |a University lecture series |v Volume 35 |w (DE-604)BV004153846 |9 35 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014158102&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014158102 | ||
Record in the Search Index
| _version_ | 1804134541030326272 |
|---|---|
| adam_text | Contents
Introduction
ix
Chapter
1.
Motivation and statement of the main results
1
1.
Characterization (l)a: Approximation with planes
2
2.
Characterization (2)a: Introducing BMO and VMO
3
3.
Multiplicative vs. additive formulation: Introducing the doubling
condition
3
4.
Characterization (l)a and flatness
4
5.
Doubling and asymptotically optimally doubling measures
7
6.
Regularity of a domain and doubling character of its harmonic measure
8
7.
Regularity of a domain and smoothness of its
Poisson
kernel
10
Chapter
2.
The relation between potential theory and geometry for
planar domains
13
1.
Smooth domains
14
2.
Non
smooth domains
15
3.
Preliminaries to the proofs of Theorems
2.7
and
2.8 20
4.
Proof of Theorem
2.7 25
5.
Proof of Theorem
2.8 29
6.
Notes
37
Chapter
3.
Preliminary results in potential theory
39
1.
Potential theory in NTA domains
39
2.
A brief review of the real variable theory of weights
46
3.
The spaces BMO and VMO
48
4.
Potential theory in C1 domains
52
5.
Notes
53
Chapter
4. Reifenberg
flat and chord arc domains
55
1.
Geometry of
Reifenberg
flat domains
55
2.
Small constant chord arc domains
61
3.
Notes
71
Chapter
5.
Further results on
Reifenberg
flat and chord arc domains
73
1.
Improved boundary regularity for
б—
Reifenberg
flat domains
74
2.
Approximation and Rellich identity
77
3.
Notes
80
Chapter
6.
From the geometry of a domain to its potential theory
81
1.
Potential theory for
Reifenberg
domains with vanishing constant
81
2.
Potential theory for vanishing chord arc domains
100
viii CONTENTS
3. Notes 112
Chapter
7.
From potential theory to the geometry of a domain
113
1.
Asymptotically optimally doubling implies
Reifenberg
vanishing
113
2.
Back to chord arc domains
124
3.
log
к
Є
VMO implies vanishing chord arc; Step I
126
4.
log
к
є
VMO implies vanishing chord arc; Step II
139
5.
Notes
146
Chapter
8.
Higher codimension and further regularity results
147
1.
Notes
151
Bibliography
153
|
| adam_txt |
Contents
Introduction
ix
Chapter
1.
Motivation and statement of the main results
1
1.
Characterization (l)a: Approximation with planes
2
2.
Characterization (2)a: Introducing BMO and VMO
3
3.
Multiplicative vs. additive formulation: Introducing the doubling
condition
3
4.
Characterization (l)a and flatness
4
5.
Doubling and asymptotically optimally doubling measures
7
6.
Regularity of a domain and doubling character of its harmonic measure
8
7.
Regularity of a domain and smoothness of its
Poisson
kernel
10
Chapter
2.
The relation between potential theory and geometry for
planar domains
13
1.
Smooth domains
14
2.
Non
smooth domains
15
3.
Preliminaries to the proofs of Theorems
2.7
and
2.8 20
4.
Proof of Theorem
2.7 25
5.
Proof of Theorem
2.8 29
6.
Notes
37
Chapter
3.
Preliminary results in potential theory
39
1.
Potential theory in NTA domains
39
2.
A brief review of the real variable theory of weights
46
3.
The spaces BMO and VMO
48
4.
Potential theory in C1 domains
52
5.
Notes
53
Chapter
4. Reifenberg
flat and chord arc domains
55
1.
Geometry of
Reifenberg
flat domains
55
2.
Small constant chord arc domains
61
3.
Notes
71
Chapter
5.
Further results on
Reifenberg
flat and chord arc domains
73
1.
Improved boundary regularity for
б—
Reifenberg
flat domains
74
2.
Approximation and Rellich identity
77
3.
Notes
80
Chapter
6.
From the geometry of a domain to its potential theory
81
1.
Potential theory for
Reifenberg
domains with vanishing constant
81
2.
Potential theory for vanishing chord arc domains
100
viii CONTENTS
3. Notes 112
Chapter
7.
From potential theory to the geometry of a domain
113
1.
Asymptotically optimally doubling implies
Reifenberg
vanishing
113
2.
Back to chord arc domains
124
3.
log
к
Є
VMO implies vanishing chord arc; Step I
126
4.
log
к
є
VMO implies vanishing chord arc; Step II
139
5.
Notes
146
Chapter
8.
Higher codimension and further regularity results
147
1.
Notes
151
Bibliography
153 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Capogna, Luca 1966- Kenig, Carlos E. 1953- Lanzani, Loredana 1965- |
| author_GND | (DE-588)132920174 (DE-588)137012624 (DE-588)173787754 |
| author_facet | Capogna, Luca 1966- Kenig, Carlos E. 1953- Lanzani, Loredana 1965- |
| author_role | aut aut aut |
| author_sort | Capogna, Luca 1966- |
| author_variant | l c lc c e k ce cek l l ll |
| building | Verbundindex |
| bvnumber | BV020836150 |
| classification_rvk | SK 560 SI 165 SK 540 |
| classification_tum | MAT 310f MAT 350f |
| ctrlnum | (OCoLC)440975405 (DE-599)BVBBV020836150 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01958nam a2200481 cb4500</leader><controlfield tag="001">BV020836150</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230821 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">051019s2005 |||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821827286</subfield><subfield code="9">0-8218-2728-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821827284</subfield><subfield code="9">978-0-8218-2728-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)440975405</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV020836150</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-824</subfield></datafield><datafield tag="080" ind1=" " ind2=" "><subfield code="a">517.9</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 560</subfield><subfield code="0">(DE-625)143246:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 165</subfield><subfield code="0">(DE-625)143085:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 310f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">28A75</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 350f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31C05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Capogna, Luca</subfield><subfield code="d">1966-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)132920174</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Harmonic measure</subfield><subfield code="b">geometric and analytic points of view</subfield><subfield code="c">Luca Capogna ; Carlos E. Kenig ; Loredana Lanzani</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, Rhode Island</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">[2005]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">x, 155 Seiten</subfield><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">University lecture series</subfield><subfield code="v">Volume 35</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonisches Maß</subfield><subfield code="0">(DE-588)4159134-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Harmonisches Maß</subfield><subfield code="0">(DE-588)4159134-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kenig, Carlos E.</subfield><subfield code="d">1953-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)137012624</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lanzani, Loredana</subfield><subfield code="d">1965-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)173787754</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-2180-9</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">University lecture series</subfield><subfield code="v">Volume 35</subfield><subfield code="w">(DE-604)BV004153846</subfield><subfield code="9">35</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014158102&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-014158102</subfield></datafield></record></collection> |
| id | DE-604.BV020836150 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:14:59Z |
| indexdate | 2024-07-09T20:26:15Z |
| institution | BVB |
| isbn | 0821827286 9780821827284 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014158102 |
| oclc_num | 440975405 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-83 DE-739 DE-11 DE-188 DE-824 |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-83 DE-739 DE-11 DE-188 DE-824 |
| physical | x, 155 Seiten Diagramme |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Capogna, Luca 1966- Verfasser (DE-588)132920174 aut Harmonic measure geometric and analytic points of view Luca Capogna ; Carlos E. Kenig ; Loredana Lanzani Providence, Rhode Island American Mathematical Society [2005] © 2005 x, 155 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 35 Harmonisches Maß (DE-588)4159134-3 gnd rswk-swf Harmonisches Maß (DE-588)4159134-3 s DE-604 Kenig, Carlos E. 1953- Verfasser (DE-588)137012624 aut Lanzani, Loredana 1965- Verfasser (DE-588)173787754 aut Erscheint auch als Online-Ausgabe 978-1-4704-2180-9 University lecture series Volume 35 (DE-604)BV004153846 35 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014158102&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Capogna, Luca 1966- Kenig, Carlos E. 1953- Lanzani, Loredana 1965- Harmonic measure geometric and analytic points of view University lecture series Harmonisches Maß (DE-588)4159134-3 gnd |
| subject_GND | (DE-588)4159134-3 |
| title | Harmonic measure geometric and analytic points of view |
| title_auth | Harmonic measure geometric and analytic points of view |
| title_exact_search | Harmonic measure geometric and analytic points of view |
| title_exact_search_txtP | Harmonic measure geometric and analytic points of view |
| title_full | Harmonic measure geometric and analytic points of view Luca Capogna ; Carlos E. Kenig ; Loredana Lanzani |
| title_fullStr | Harmonic measure geometric and analytic points of view Luca Capogna ; Carlos E. Kenig ; Loredana Lanzani |
| title_full_unstemmed | Harmonic measure geometric and analytic points of view Luca Capogna ; Carlos E. Kenig ; Loredana Lanzani |
| title_short | Harmonic measure |
| title_sort | harmonic measure geometric and analytic points of view |
| title_sub | geometric and analytic points of view |
| topic | Harmonisches Maß (DE-588)4159134-3 gnd |
| topic_facet | Harmonisches Maß |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014158102&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
| work_keys_str_mv | AT capognaluca harmonicmeasuregeometricandanalyticpointsofview AT kenigcarlose harmonicmeasuregeometricandanalyticpointsofview AT lanzaniloredana harmonicmeasuregeometricandanalyticpointsofview |