The Fatou Property for General Approximate Identities on Metric Measure Spaces
approximate identities on metric measure spaces are considered in this paper. We find exact conditions on the geometry of domains for which the convergence of approximate identities occurs almost everywhere for functions from the spaces , . The results are illustrated with examples of Poisson kernel...
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| Veröffentlicht in: | Mathematical Notes 2021-07, Vol.110 (1-2), p.196-209 |
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| creator | Karagulyan, G. A. Katkovskaya, I. N. Krotov, V. G. |
| description | approximate identities on metric measure spaces are considered in this paper. We find exact conditions on the geometry of domains for which the convergence of approximate identities occurs almost everywhere for functions from the spaces
,
. The results are illustrated with examples of Poisson kernels and their powers in the unit ball in
or
, and also of convolutions with dilatations on
. In all these examples, the conditions found are exact. |
| doi_str_mv | 10.1134/S000143462107021X |
| format | Article |
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,
. The results are illustrated with examples of Poisson kernels and their powers in the unit ball in
or
, and also of convolutions with dilatations on
. In all these examples, the conditions found are exact.</description><identifier>ISSN: 0001-4346</identifier><identifier>ISSN: 1067-9073</identifier><identifier>EISSN: 1573-8876</identifier><identifier>DOI: 10.1134/S000143462107021X</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>14/34 ; 639/766/189 ; 639/766/530 ; 639/766/747 ; Mathematics ; Mathematics and Statistics</subject><ispartof>Mathematical Notes, 2021-07, Vol.110 (1-2), p.196-209</ispartof><rights>Pleiades Publishing, Ltd. 2021</rights><rights>Pleiades Publishing, Ltd. 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c198t-fa6f6cb67140caf85c322e4861d97fa26afb718a601bf6a71afcce78f02180ff3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S000143462107021X$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S000143462107021X$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Karagulyan, G. A.</creatorcontrib><creatorcontrib>Katkovskaya, I. N.</creatorcontrib><creatorcontrib>Krotov, V. G.</creatorcontrib><title>The Fatou Property for General Approximate Identities on Metric Measure Spaces</title><title>Mathematical Notes</title><addtitle>Math Notes</addtitle><description>approximate identities on metric measure spaces are considered in this paper. We find exact conditions on the geometry of domains for which the convergence of approximate identities occurs almost everywhere for functions from the spaces
,
. The results are illustrated with examples of Poisson kernels and their powers in the unit ball in
or
, and also of convolutions with dilatations on
. In all these examples, the conditions found are exact.</description><subject>14/34</subject><subject>639/766/189</subject><subject>639/766/530</subject><subject>639/766/747</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0001-4346</issn><issn>1067-9073</issn><issn>1573-8876</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1UEtLAzEQDqJgrf4AbwHPq5nsNskeS7EPqA9oBW9Lmk50S92sSRbsvzdLBQ_iaRi-x8z3EXIN7BYgL-5WjDEo8kJwYJJxeD0hAxjJPFNKilMy6OGsx8_JRQi7tIEANiCP63ekUx1dR5-9a9HHA7XO0xk26PWejtvWu6_6Q0ekiy02sY41Buoa-oDR1yYNHTqPdNVqg-GSnFm9D3j1M4fkZXq_nsyz5dNsMRkvMwOlipnVwgqzERIKZrRVI5NzjoUSsC2l1Vxou5GgtGCwsUJL0NYYlMqmZIpZmw_JzdE3fffZYYjVznW-SScrPhK5LEEWMrHgyDLeheDRVq1PUfyhAlb1tVV_aksaftSExG3e0P86_y_6BriebtM</recordid><startdate>20210701</startdate><enddate>20210701</enddate><creator>Karagulyan, G. A.</creator><creator>Katkovskaya, I. N.</creator><creator>Krotov, V. G.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210701</creationdate><title>The Fatou Property for General Approximate Identities on Metric Measure Spaces</title><author>Karagulyan, G. A. ; Katkovskaya, I. N. ; Krotov, V. G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c198t-fa6f6cb67140caf85c322e4861d97fa26afb718a601bf6a71afcce78f02180ff3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>14/34</topic><topic>639/766/189</topic><topic>639/766/530</topic><topic>639/766/747</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Karagulyan, G. A.</creatorcontrib><creatorcontrib>Katkovskaya, I. N.</creatorcontrib><creatorcontrib>Krotov, V. G.</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematical Notes</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Karagulyan, G. A.</au><au>Katkovskaya, I. N.</au><au>Krotov, V. G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Fatou Property for General Approximate Identities on Metric Measure Spaces</atitle><jtitle>Mathematical Notes</jtitle><stitle>Math Notes</stitle><date>2021-07-01</date><risdate>2021</risdate><volume>110</volume><issue>1-2</issue><spage>196</spage><epage>209</epage><pages>196-209</pages><issn>0001-4346</issn><issn>1067-9073</issn><eissn>1573-8876</eissn><abstract>approximate identities on metric measure spaces are considered in this paper. We find exact conditions on the geometry of domains for which the convergence of approximate identities occurs almost everywhere for functions from the spaces
,
. The results are illustrated with examples of Poisson kernels and their powers in the unit ball in
or
, and also of convolutions with dilatations on
. In all these examples, the conditions found are exact.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S000143462107021X</doi><tpages>14</tpages></addata></record> |
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| title | The Fatou Property for General Approximate Identities on Metric Measure Spaces |
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