On the Sobolev Dolbeault cohomology of a domain with pseudoconcave boundaries
In this note, we mainly make use of a method devised by Shaw [15] for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type Ω = Ω ˜ \ ∪ j = 1 m Ω j ¯ , where Ω ˜ and { Ω j } j = 1 m ⋐ Ω ~ are bounded pseudoconvex domains in ℂ n with smooth boundaries, and Ω ¯ 1 , ⋯ , Ω ¯ m ar...
Saved in:
| Published in | Acta mathematica scientia Vol. 44; no. 2; pp. 431 - 444 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Singapore
Springer Nature Singapore
01.03.2024
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In this note, we mainly make use of a method devised by Shaw [15] for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type
Ω
=
Ω
˜
\
∪
j
=
1
m
Ω
j
¯
, where
Ω
˜
and
{
Ω
j
}
j
=
1
m
⋐
Ω
~
are bounded pseudoconvex domains in ℂ
n
with smooth boundaries, and
Ω
¯
1
,
⋯
,
Ω
¯
m
are mutually disjoint. The main results can also be quickly obtained by virtue of [5]. |
|---|---|
| AbstractList | In this note, we mainly make use of a method devised by Shaw [15] for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type
Ω
=
Ω
˜
\
∪
j
=
1
m
Ω
j
¯
, where
Ω
˜
and
{
Ω
j
}
j
=
1
m
⋐
Ω
~
are bounded pseudoconvex domains in ℂ
n
with smooth boundaries, and
Ω
¯
1
,
⋯
,
Ω
¯
m
are mutually disjoint. The main results can also be quickly obtained by virtue of [5]. 32W05%32A36%35N15; In this note,we mainly make use of a method devised by Shaw[15]for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type Ω=(Ω)\(∪mj=1Ωj),where(Ω)and {Ωj }mj=1(∈)(Ω)are bounded pseudoconvex domains in Cn with smooth boundaries,and(Ω)1,…,(Ω)m are mutually disjoint.The main results can also be quickly obtained by virtue of[5]. |
| Author | Chen, Jian |
| Author_xml | – sequence: 1 givenname: Jian surname: Chen fullname: Chen, Jian email: jian-chen@whu.edu.cn organization: School of Mathematics and Statistics, Wuhan University |
| BookMark | eNp1kD1rwzAQhkVJoUnaH9BNawe355MlJWNJPyElQ7ML2ZYSB0cKlp2Pf18ZFzp1OO6G570XngkZOe8MIfcpPKYA8imkkEmWAGZxgCV4RcYpl5jMYSZHZAzI4y0Ab8gkhB1AKlBkY_K1crTdGvrtc1-bI33xdW50V7e08Fu_97XfXKi3VNPS73Xl6Klqt_QQTFf6wrtCHw3NfedK3VQm3JJrq-tg7n73lKzfXteLj2S5ev9cPC-TAmXWJgiWYy4KzvMZQyEMY2VuZrLkeSznoG3J51xYFGAynVmpWSExM6VEAIZsSh6GtyftrHYbtfNd42KhCudTfc6VwSgCejiy6cAWjQ-hMVYdmmqvm4tKQfXq1KBOxYTq1an-Pw6ZEFm3Mc1fwf-hH5GGcyE |
| Cites_doi | 10.1090/conm/550/10872 10.1007/BF01455965 10.1090/tran/6547 10.1090/conm/644/12780 10.1007/978-3-642-65217-2 10.1007/978-3-0346-0009-5_19 10.1512/iumj.2018.67.7307 10.1007/s00209-012-1111-z 10.1007/s00209-021-02750-6 10.1007/BF02391775 10.1016/S0007-4497(00)00126-3 10.1090/amsip/019 10.4310/PAMQ.2022.v18.n2.a7 10.1090/S0002-9947-2012-05511-5 10.4171/076 |
| ClassificationCodes | 32W05%32A36%35N15 |
| ContentType | Journal Article |
| Copyright | Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences 2024 Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
| Copyright_xml | – notice: Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences 2024 – notice: Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
| DBID | AAYXX CITATION 2B. 4A8 92I 93N PSX TCJ |
| DOI | 10.1007/s10473-024-0203-2 |
| DatabaseName | CrossRef Wanfang Data Journals - Hong Kong WANFANG Data Centre Wanfang Data Journals 万方数据期刊 - 香港版 China Online Journals (COJ) China Online Journals (COJ) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics Physics |
| EISSN | 1572-9087 |
| EndPage | 444 |
| ExternalDocumentID | sxwlxb_e202402003 10_1007_s10473_024_0203_2 |
| GroupedDBID | --K --M -01 -0A -EM -SA -S~ .~1 0R~ 1B1 1~. 1~5 23M 2B. 2C. 4.4 406 457 4G. 5GY 5VR 5VS 5XA 5XB 7-5 71M 8P~ 92E 92I 92M 92Q 93N 9D9 9DA AACDK AACTN AAEDT AAEDW AAHNG AAIKJ AAJBT AAKOC AALRI AAOAW AASML AATNV AAUYE AAXDM AAXKI AAXUO ABAKF ABAOU ABECU ABFNM ABFTV ABJNI ABKCH ABMAC ABMQK ABTEG ABTKH ABTMW ABWVN ABXDB ABXPI ACAOD ACDAQ ACDTI ACGFS ACHSB ACMLO ACOKC ACPIV ACRLP ACRPL ACZOJ ADBBV ADEZE ADKNI ADMUD ADNMO ADTPH ADURQ ADYFF AEBSH AEFQL AEIPS AEJRE AEKER AEMSY AENEX AESKC AFBBN AFKWA AFQWF AFUIB AGDGC AGHFR AGJBK AGMZJ AGQEE AGUBO AGYEJ AIAKS AIEXJ AIGIU AIGVJ AIKHN AILAN AITGF AITUG AJOXV AJZVZ AKRWK ALMA_UNASSIGNED_HOLDINGS AMFUW AMKLP AMRAJ AMXSW AMYLF ANKPU ARUGR AXJTR AXYYD BGNMA BKOJK BLXMC CAJEA CCEZO CCVFK CHBEP CS3 CSCUP CW9 DPUIP EBLON EBS EFJIC EJD EO9 EP2 EP3 FA0 FDB FEDTE FIGPU FIRID FNLPD FNPLU FYGXN GBLVA GJIRD HG6 HVGLF HZ~ IKXTQ IWAJR J1W JUIAU JZLTJ KOM KOV LLZTM M41 M4Y MHUIS MO0 N9A NPVJJ NQJWS NU0 O-L O9- OAUVE OZT P-8 P-9 P2P PC. PT4 Q-- Q-0 Q38 R-A REI RIG ROL RSV RT1 S.. SDC SDF SDG SDH SES SJYHP SNE SNPRN SOHCF SOJ SPC SRMVM SSLCW SSW SSZ T5K T8Q TCJ TGP TSG U1F U1G U5A U5K UOJIU UTJUX VEKWB VFIZW ZMTXR ~G- ~L9 AATTM AAYWO AAYXX ABBRH ABDBE ABFSG ACSTC ACVFH ADCNI AEUPX AEZWR AFDZB AFHIU AFOHR AFPUW AFXIZ AGCQF AGRNS AHPBZ AHWEU AIGII AIIUN AIXLP AKBMS AKYEP ATHPR AYFIA CITATION SSH 4A8 PSX |
| ID | FETCH-LOGICAL-c274t-20f52b6c55b83266e33dbe87d5bbea50afd5956f260e4a4f7a3c724ed7200323 |
| ISSN | 0252-9602 |
| IngestDate | Thu May 29 04:00:09 EDT 2025 Tue Jul 01 02:27:42 EDT 2025 Fri Feb 21 02:40:20 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | 32A36 Neumann operator 35N15 Bergman spaces 32W05 Cauchy-Riemann equations pseudoconcave domains (?)-Neumann operator |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c274t-20f52b6c55b83266e33dbe87d5bbea50afd5956f260e4a4f7a3c724ed7200323 |
| PageCount | 14 |
| ParticipantIDs | wanfang_journals_sxwlxb_e202402003 crossref_primary_10_1007_s10473_024_0203_2 springer_journals_10_1007_s10473_024_0203_2 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2024-03-01 |
| PublicationDateYYYYMMDD | 2024-03-01 |
| PublicationDate_xml | – month: 03 year: 2024 text: 2024-03-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Singapore |
| PublicationPlace_xml | – name: Singapore |
| PublicationTitle | Acta mathematica scientia |
| PublicationTitleAbbrev | Acta Math Sci |
| PublicationTitle_FL | Acta Mathematica Scientia |
| PublicationYear | 2024 |
| Publisher | Springer Nature Singapore |
| Publisher_xml | – name: Springer Nature Singapore |
| References | Chakrabarti, Shaw (CR4) 2012; 364 Straube (CR17) 2010 Huang, Li (CR9) 2016; 368 Laurent-Thiébaut, Leiterer (CR10) 2000; 124 Chen, Shaw (CR6) 2001 Lions, Magenes (CR13) 1972 Chakrabarti, Laurent-Thiébaut, Shaw (CR3) 2018; 67 Li, Shaw (CR12) 2013; 8 Chakrabarti, Harrington (CR5) 2021; 299 Laurent-Thiébaut, Shaw (CR11) 2013; 274 Shaw, Barkatou, Berhanu, Meziani (CR15) 2011 CR18 Shaw, Feehan, Song, Weinkove, Wentworth (CR16) 2015 Boas (CR2) 1987; 300 Hörmander (CR8) 1965; 113 Shaw, Ebenfelt, Hunger-bühler, Kohn (CR14) 2010 Fu, Shaw (CR7) 2022; 18 Bell, Boas (CR1) 1984; 267 S C Chen (203_CR6) 2001 M C Shaw (203_CR14) 2010 E J Straube (203_CR17) 2010 D Chakrabarti (203_CR3) 2018; 67 S Q Fu (203_CR7) 2022; 18 M C Shaw (203_CR16) 2015 203_CR18 L Hörmander (203_CR8) 1965; 113 D Chakrabarti (203_CR4) 2012; 364 M C Shaw (203_CR15) 2011 D Chakrabarti (203_CR5) 2021; 299 C Laurent-Thiébaut (203_CR11) 2013; 274 X S Li (203_CR12) 2013; 8 H P Boas (203_CR2) 1987; 300 S R Bell (203_CR1) 1984; 267 J L Lions (203_CR13) 1972 C Laurent-Thiébaut (203_CR10) 2000; 124 X J Huang (203_CR9) 2016; 368 |
| References_xml | – start-page: 161 year: 2011 end-page: 171 ident: CR15 article-title: Duality between harmonic and Bergman spaces publication-title: Geometric Analysis of Several Complex Variables and Related Topics doi: 10.1090/conm/550/10872 – volume: 267 start-page: 473 year: 1984 end-page: 478 ident: CR1 article-title: Regularity of the Bergman projection and duality of holomorphic function spaces publication-title: Math Ann doi: 10.1007/BF01455965 – ident: CR18 – volume: 368 start-page: 6915 year: 2016 end-page: 6937 ident: CR9 article-title: -equation on a lunar domain with mixed boundary conditions publication-title: Trans Amer Math Soc doi: 10.1090/tran/6547 – volume: 8 start-page: 399 year: 2013 end-page: 411 ident: CR12 article-title: The ∂-equation on an annulus with mixed boundary conditions publication-title: Bull Inst Math Acad Sin – start-page: 211 year: 2015 end-page: 225 ident: CR16 article-title: Topology of Dolbeault cohomology groups publication-title: Analysis, Complex Geometry, and Mathematical Physics: In Honor of Duong H. Phong doi: 10.1090/conm/644/12780 – year: 1972 ident: CR13 publication-title: Non-Homogeneous Boundary Value Problems and Applications: Volume I doi: 10.1007/978-3-642-65217-2 – start-page: 307 year: 2010 end-page: 320 ident: CR14 article-title: The closed range property for ∂ on domains with pseudoconcave boundary publication-title: Complex Analysis doi: 10.1007/978-3-0346-0009-5_19 – volume: 67 start-page: 831 year: 2018 end-page: 857 ident: CR3 article-title: On the -Dolbeault cohomology of annuli publication-title: Indiana Univ Math J doi: 10.1512/iumj.2018.67.7307 – volume: 274 start-page: 1165 year: 2013 end-page: 1176 ident: CR11 article-title: On the Hausdorff property of some Dolbeault cohomology groups publication-title: Math Z doi: 10.1007/s00209-012-1111-z – volume: 300 start-page: 109 year: 1987 end-page: 132 ident: CR2 article-title: The Szego projection: Sobolev estimates in regular domains publication-title: Trans Amer Math Soc – year: 2010 ident: CR17 publication-title: Lectures on the -Sobolev theory of the -Neumann problem – volume: 299 start-page: 1837 year: 2021 end-page: 1873 ident: CR5 article-title: Exact sequences and estimates for the -problem publication-title: Math Z doi: 10.1007/s00209-021-02750-6 – volume: 113 start-page: 89 year: 1965 end-page: 152 ident: CR8 article-title: estimates and existence theorems for the operator publication-title: Acta Math doi: 10.1007/BF02391775 – volume: 124 start-page: 93 year: 2000 end-page: 106 ident: CR10 article-title: On Serre duality publication-title: Bull Sci Math doi: 10.1016/S0007-4497(00)00126-3 – year: 2001 ident: CR6 publication-title: Partial differential equations in several complex variables doi: 10.1090/amsip/019 – volume: 18 start-page: 503 year: 2022 end-page: 529 ident: CR7 article-title: Sobolev estimates and duality for on domains in ℂ publication-title: Pure Appl Math Q doi: 10.4310/PAMQ.2022.v18.n2.a7 – volume: 364 start-page: 3529 year: 2012 end-page: 3554 ident: CR4 article-title: Serre duality on domains in complex manifolds and applications publication-title: Trans Amer Math Soc doi: 10.1090/S0002-9947-2012-05511-5 – volume: 267 start-page: 473 year: 1984 ident: 203_CR1 publication-title: Math Ann doi: 10.1007/BF01455965 – volume: 364 start-page: 3529 year: 2012 ident: 203_CR4 publication-title: Trans Amer Math Soc doi: 10.1090/S0002-9947-2012-05511-5 – volume: 113 start-page: 89 year: 1965 ident: 203_CR8 publication-title: Acta Math doi: 10.1007/BF02391775 – volume: 8 start-page: 399 year: 2013 ident: 203_CR12 publication-title: Bull Inst Math Acad Sin – ident: 203_CR18 – volume: 299 start-page: 1837 year: 2021 ident: 203_CR5 publication-title: Math Z doi: 10.1007/s00209-021-02750-6 – volume: 18 start-page: 503 year: 2022 ident: 203_CR7 publication-title: Pure Appl Math Q doi: 10.4310/PAMQ.2022.v18.n2.a7 – start-page: 307 volume-title: Complex Analysis year: 2010 ident: 203_CR14 doi: 10.1007/978-3-0346-0009-5_19 – start-page: 161 volume-title: Geometric Analysis of Several Complex Variables and Related Topics year: 2011 ident: 203_CR15 doi: 10.1090/conm/550/10872 – volume: 300 start-page: 109 year: 1987 ident: 203_CR2 publication-title: Trans Amer Math Soc – volume: 274 start-page: 1165 year: 2013 ident: 203_CR11 publication-title: Math Z doi: 10.1007/s00209-012-1111-z – volume: 67 start-page: 831 year: 2018 ident: 203_CR3 publication-title: Indiana Univ Math J doi: 10.1512/iumj.2018.67.7307 – volume-title: Partial differential equations in several complex variables year: 2001 ident: 203_CR6 doi: 10.1090/amsip/019 – volume: 124 start-page: 93 year: 2000 ident: 203_CR10 publication-title: Bull Sci Math doi: 10.1016/S0007-4497(00)00126-3 – volume: 368 start-page: 6915 year: 2016 ident: 203_CR9 publication-title: Trans Amer Math Soc doi: 10.1090/tran/6547 – start-page: 211 volume-title: Analysis, Complex Geometry, and Mathematical Physics: In Honor of Duong H. Phong year: 2015 ident: 203_CR16 doi: 10.1090/conm/644/12780 – volume-title: Lectures on the L 2-Sobolev theory of the $${\bar \partial }$$-Neumann problem year: 2010 ident: 203_CR17 doi: 10.4171/076 – volume-title: Non-Homogeneous Boundary Value Problems and Applications: Volume I year: 1972 ident: 203_CR13 doi: 10.1007/978-3-642-65217-2 |
| SSID | ssj0016264 |
| Score | 2.300812 |
| Snippet | In this note, we mainly make use of a method devised by Shaw [15] for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type
Ω
=
Ω
˜
\
∪... 32W05%32A36%35N15; In this note,we mainly make use of a method devised by Shaw[15]for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the... |
| SourceID | wanfang crossref springer |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 431 |
| SubjectTerms | Analysis Mathematics Mathematics and Statistics |
| Title | On the Sobolev Dolbeault cohomology of a domain with pseudoconcave boundaries |
| URI | https://link.springer.com/article/10.1007/s10473-024-0203-2 https://d.wanfangdata.com.cn/periodical/sxwlxb-e202402003 |
| Volume | 44 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3db9MwELeqTUjwwMcAMb5kIfxCFdQ6cew8OqmrbmoTxNppb1E-HF5QQLQTE38958RJWg2hwUuUxtc4uvv5fJf7CELvi6IwVql2ChpUjpdz18kyxh1e8WlZBmWRNR34VrG_2HjnV-xqNDrby1q63uUfi19_rCv5H6nCNZCrqZL9B8n2N4ULcA7yhSNIGI53knESNxk7F0mYLNXleJYsQyU3y_U4ShbJqgkRmaweCSMreWYaaK8X408XajNLoiSO5KUah8kmnsnPnVFozVSifBIwEk6IYkTOiPSJ4kQERAbmJJgQ4e8N-URIIhlRcxJGRAiiBBEhCafNfWCU27-boZamf_9wbjRMtFDx_vsH6g0JWFZNUUYd8IMOdGrb09Fih-4pSM_q_Hav9Vq6W2p80pU1e9xEmWFOCrPSYc_qMwm3Nz-_3uSpNk82afu-HlPwGEDlHct5GMZ9SAk8t6aXWPe4XYi7raM8nOjQSOki5E1dV11l9Zc9E2T9GD20vgOWLRCeoJGuT9Aj60dgq6W3J-jBqu_FC7_uNUm-xfYpgu0TA16wxQvu8YIHvOBkjiVu8YINXvABXvCAl2doPVfraOHYz2nAOuTeDlZOxWjuF4zloMZ9X7tumWvBS5bnOmOTrCoZeMsVeLjay7yKZ27BqadLbvhK3efoqP5W6xcIu5UIdGDaWpYmcJ-JjFEtiioPpuCw8ekp-tCxL_3eNk1Jh_bYhtcp8Do1vE7pKRp3DE7t2tr-jfqdlcFAfAsDL-9C9ArdH-D8Gh3tflzrN2Bg7vK3Fjq_AQG8W3M |
| linkProvider | Library Specific Holdings |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=ON+THE+SOBOLEV+DOLBEAULT+COHOMOLOGY+OF+A+DOMAIN+WITH+PSEUDOCONCAVE+BOUNDARIES&rft.jtitle=%E6%95%B0%E5%AD%A6%E7%89%A9%E7%90%86%E5%AD%A6%E6%8A%A5%EF%BC%88%E8%8B%B1%E6%96%87%E7%89%88%EF%BC%89&rft.au=Jian+CHEN&rft.date=2024-03-01&rft.issn=0252-9602&rft.volume=44&rft.issue=2&rft.spage=431&rft.epage=444&rft_id=info:doi/10.1007%2Fs10473-024-0203-2&rft.externalDocID=sxwlxb_e202402003 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fwww.wanfangdata.com.cn%2Fimages%2FPeriodicalImages%2Fsxwlxb-e%2Fsxwlxb-e.jpg |