Absolutely continuous mappings on doubling metric measure spaces
We consider Q -absolutely continuous mappings f : X → V between a doubling metric measure space X and a Banach space V . The relation between these mappings and Sobolev mappings f ∈ N 1 , p ( X ; V ) for p ≥ Q ≥ 1 is investigated. In particular, a locally Q -absolutely continuous mapping on an Ahlfo...
Gespeichert in:
| Veröffentlicht in: | Manuscripta mathematica 2024-01, Vol.173 (1-2), p.1-21 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 21 |
|---|---|
| container_issue | 1-2 |
| container_start_page | 1 |
| container_title | Manuscripta mathematica |
| container_volume | 173 |
| creator | Lahti, Panu Zhou, Xiaodan |
| description | We consider
Q
-absolutely continuous mappings
f
:
X
→
V
between a doubling metric measure space
X
and a Banach space
V
. The relation between these mappings and Sobolev mappings
f
∈
N
1
,
p
(
X
;
V
)
for
p
≥
Q
≥
1
is investigated. In particular, a locally
Q
-absolutely continuous mapping on an Ahlfors
Q
-regular space is a continuous mapping in
N
loc
1
,
Q
(
X
;
V
)
, as well as differentiable almost everywhere in terms of Cheeger derivatives provided
V
satisfies the Radon-Nikodym property. Conversely, though a continuous Sobolev mapping
f
∈
N
loc
1
,
Q
(
X
;
V
)
is generally not locally
Q
-absolutely continuous, this implication holds if
f
is further assumed to be pseudomonotone. It follows that pseudomonotone mappings satisfying a relaxed quasiconformality condition are also
Q
-absolutely continuous. |
| doi_str_mv | 10.1007/s00229-023-01460-z |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2909669194</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2909669194</sourcerecordid><originalsourceid>FETCH-LOGICAL-c380t-cc8a4a6fe1b365bc75504d8b848f632d4d621b4e721bad0bdfbc6a5bc11474983</originalsourceid><addsrcrecordid>eNp9kE9LxDAQxYMouK5-AU8Fz9HJn6bpzWXRVVjwoueQpOnSpdvUpDnsfnqjFbx5mccwv_cGHkK3BO4JQPUQASitMVCGgXAB-HSGFoQzikkly3O0yPcSU0HIJbqKcQ-ZYhVboMeVib5Pk-uPhfXD1A3Jp1gc9Dh2wy4Wfigan0yfl-LgptDZLDqm4Io4auviNbpodR_dza8u0cfz0_v6BW_fNq_r1RZbJmHC1krNtWgdMUyUxlZlCbyRRnLZCkYb3ghKDHdVnroB07TGCp1BQnjFa8mW6G7OHYP_TC5Oau9TGPJLRWuohahJzTNFZ8oGH2NwrRpDd9DhqAio76bU3JTKTamfptQpm9hsihkedi78Rf_j-gJfQ2zr</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2909669194</pqid></control><display><type>article</type><title>Absolutely continuous mappings on doubling metric measure spaces</title><source>Springer Nature - Complete Springer Journals</source><creator>Lahti, Panu ; Zhou, Xiaodan</creator><creatorcontrib>Lahti, Panu ; Zhou, Xiaodan</creatorcontrib><description>We consider
Q
-absolutely continuous mappings
f
:
X
→
V
between a doubling metric measure space
X
and a Banach space
V
. The relation between these mappings and Sobolev mappings
f
∈
N
1
,
p
(
X
;
V
)
for
p
≥
Q
≥
1
is investigated. In particular, a locally
Q
-absolutely continuous mapping on an Ahlfors
Q
-regular space is a continuous mapping in
N
loc
1
,
Q
(
X
;
V
)
, as well as differentiable almost everywhere in terms of Cheeger derivatives provided
V
satisfies the Radon-Nikodym property. Conversely, though a continuous Sobolev mapping
f
∈
N
loc
1
,
Q
(
X
;
V
)
is generally not locally
Q
-absolutely continuous, this implication holds if
f
is further assumed to be pseudomonotone. It follows that pseudomonotone mappings satisfying a relaxed quasiconformality condition are also
Q
-absolutely continuous.</description><identifier>ISSN: 0025-2611</identifier><identifier>EISSN: 1432-1785</identifier><identifier>DOI: 10.1007/s00229-023-01460-z</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebraic Geometry ; Banach spaces ; Calculus of Variations and Optimal Control; Optimization ; Geometry ; Lie Groups ; Mapping ; Mathematics ; Mathematics and Statistics ; Number Theory ; Topological Groups</subject><ispartof>Manuscripta mathematica, 2024-01, Vol.173 (1-2), p.1-21</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c380t-cc8a4a6fe1b365bc75504d8b848f632d4d621b4e721bad0bdfbc6a5bc11474983</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00229-023-01460-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00229-023-01460-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Lahti, Panu</creatorcontrib><creatorcontrib>Zhou, Xiaodan</creatorcontrib><title>Absolutely continuous mappings on doubling metric measure spaces</title><title>Manuscripta mathematica</title><addtitle>manuscripta math</addtitle><description>We consider
Q
-absolutely continuous mappings
f
:
X
→
V
between a doubling metric measure space
X
and a Banach space
V
. The relation between these mappings and Sobolev mappings
f
∈
N
1
,
p
(
X
;
V
)
for
p
≥
Q
≥
1
is investigated. In particular, a locally
Q
-absolutely continuous mapping on an Ahlfors
Q
-regular space is a continuous mapping in
N
loc
1
,
Q
(
X
;
V
)
, as well as differentiable almost everywhere in terms of Cheeger derivatives provided
V
satisfies the Radon-Nikodym property. Conversely, though a continuous Sobolev mapping
f
∈
N
loc
1
,
Q
(
X
;
V
)
is generally not locally
Q
-absolutely continuous, this implication holds if
f
is further assumed to be pseudomonotone. It follows that pseudomonotone mappings satisfying a relaxed quasiconformality condition are also
Q
-absolutely continuous.</description><subject>Algebraic Geometry</subject><subject>Banach spaces</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Geometry</subject><subject>Lie Groups</subject><subject>Mapping</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><subject>Topological Groups</subject><issn>0025-2611</issn><issn>1432-1785</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LxDAQxYMouK5-AU8Fz9HJn6bpzWXRVVjwoueQpOnSpdvUpDnsfnqjFbx5mccwv_cGHkK3BO4JQPUQASitMVCGgXAB-HSGFoQzikkly3O0yPcSU0HIJbqKcQ-ZYhVboMeVib5Pk-uPhfXD1A3Jp1gc9Dh2wy4Wfigan0yfl-LgptDZLDqm4Io4auviNbpodR_dza8u0cfz0_v6BW_fNq_r1RZbJmHC1krNtWgdMUyUxlZlCbyRRnLZCkYb3ghKDHdVnroB07TGCp1BQnjFa8mW6G7OHYP_TC5Oau9TGPJLRWuohahJzTNFZ8oGH2NwrRpDd9DhqAio76bU3JTKTamfptQpm9hsihkedi78Rf_j-gJfQ2zr</recordid><startdate>20240101</startdate><enddate>20240101</enddate><creator>Lahti, Panu</creator><creator>Zhou, Xiaodan</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240101</creationdate><title>Absolutely continuous mappings on doubling metric measure spaces</title><author>Lahti, Panu ; Zhou, Xiaodan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c380t-cc8a4a6fe1b365bc75504d8b848f632d4d621b4e721bad0bdfbc6a5bc11474983</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algebraic Geometry</topic><topic>Banach spaces</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Geometry</topic><topic>Lie Groups</topic><topic>Mapping</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><topic>Topological Groups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lahti, Panu</creatorcontrib><creatorcontrib>Zhou, Xiaodan</creatorcontrib><collection>CrossRef</collection><jtitle>Manuscripta mathematica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lahti, Panu</au><au>Zhou, Xiaodan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Absolutely continuous mappings on doubling metric measure spaces</atitle><jtitle>Manuscripta mathematica</jtitle><stitle>manuscripta math</stitle><date>2024-01-01</date><risdate>2024</risdate><volume>173</volume><issue>1-2</issue><spage>1</spage><epage>21</epage><pages>1-21</pages><issn>0025-2611</issn><eissn>1432-1785</eissn><abstract>We consider
Q
-absolutely continuous mappings
f
:
X
→
V
between a doubling metric measure space
X
and a Banach space
V
. The relation between these mappings and Sobolev mappings
f
∈
N
1
,
p
(
X
;
V
)
for
p
≥
Q
≥
1
is investigated. In particular, a locally
Q
-absolutely continuous mapping on an Ahlfors
Q
-regular space is a continuous mapping in
N
loc
1
,
Q
(
X
;
V
)
, as well as differentiable almost everywhere in terms of Cheeger derivatives provided
V
satisfies the Radon-Nikodym property. Conversely, though a continuous Sobolev mapping
f
∈
N
loc
1
,
Q
(
X
;
V
)
is generally not locally
Q
-absolutely continuous, this implication holds if
f
is further assumed to be pseudomonotone. It follows that pseudomonotone mappings satisfying a relaxed quasiconformality condition are also
Q
-absolutely continuous.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00229-023-01460-z</doi><tpages>21</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-2611 |
| ispartof | Manuscripta mathematica, 2024-01, Vol.173 (1-2), p.1-21 |
| issn | 0025-2611 1432-1785 |
| language | eng |
| recordid | cdi_proquest_journals_2909669194 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebraic Geometry Banach spaces Calculus of Variations and Optimal Control Optimization Geometry Lie Groups Mapping Mathematics Mathematics and Statistics Number Theory Topological Groups |
| title | Absolutely continuous mappings on doubling metric measure spaces |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-12T20%3A11%3A23IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Absolutely%20continuous%20mappings%20on%20doubling%20metric%20measure%20spaces&rft.jtitle=Manuscripta%20mathematica&rft.au=Lahti,%20Panu&rft.date=2024-01-01&rft.volume=173&rft.issue=1-2&rft.spage=1&rft.epage=21&rft.pages=1-21&rft.issn=0025-2611&rft.eissn=1432-1785&rft_id=info:doi/10.1007/s00229-023-01460-z&rft_dat=%3Cproquest_cross%3E2909669194%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2909669194&rft_id=info:pmid/&rfr_iscdi=true |