Boundedness of vector-valued Calderón-Zygmund operators on non-homogeneous metric measure spaces
Let ( X , d , μ ) be a non-homogeneous metric measure space and satisfies non-atomic condition that μ ( { x } ) = 0 for all x ∈ X . B 1 and B 2 are Banach spaces. In this paper, we show that the boundedness of the vector-valued Calderón-Zygmund operator T → from L 2 ( X , B 1 ) to L 2 ( X , B 2 ) is...
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| Veröffentlicht in: | Journal of pseudo-differential operators and applications 2022-09, Vol.13 (3), Article 36 |
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| creator | Han, Yaoyao |
| description | Let
(
X
,
d
,
μ
)
be a non-homogeneous metric measure space and satisfies non-atomic condition that
μ
(
{
x
}
)
=
0
for all
x
∈
X
.
B
1
and
B
2
are Banach spaces. In this paper, we show that the boundedness of the vector-valued Calderón-Zygmund operator
T
→
from
L
2
(
X
,
B
1
)
to
L
2
(
X
,
B
2
)
is equivalent to
T
→
from
L
p
(
X
,
B
1
)
to
L
p
(
X
,
B
2
)
for
p
∈
(
1
,
∞
)
, and from
L
1
(
X
,
B
1
)
to
L
1
,
∞
(
X
,
B
2
)
. As an application, we prove that if
T
→
is bounded from
L
2
(
X
,
B
1
)
to
L
2
(
X
,
B
2
)
, then its maximal operator is bounded from
L
p
(
X
,
B
1
)
to
L
p
(
X
,
B
2
)
for
p
∈
(
1
,
∞
)
and from
L
1
(
X
,
B
1
)
to
L
1
,
∞
(
X
,
B
2
)
. |
| doi_str_mv | 10.1007/s11868-022-00468-5 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2686903498</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2686903498</sourcerecordid><originalsourceid>FETCH-LOGICAL-c249t-1faf613fe87f01137c894917cffb1801fd5ee7af534581673198d600ec14ac583</originalsourceid><addsrcrecordid>eNp9kM1KAzEUhYMoWGpfwNWA62juZH6SpRb_oOBGQdyEmLmpLZ1kTGYKfS4fwRczdUR33s25i--cezmEnAI7B8bqiwggKkFZnlPGirSVB2QCVZVTKeXz4e8u4JjMYlyzNFxyAD4h-soPrsHGYYyZt9kWTe8D3erNgE0215sGw-eHoy-7ZZvAzHcYdCIS7DLnHX3zrV-iQz_ErMU-rEwSHYeAWey0wXhCjqzeRJz96JQ83Vw_zu_o4uH2fn65oCYvZE_BalsBtyhqy9JrtRGykFAba19BMLBNiVhrW_KiFFDVHKRoKsbQQKFNKfiUnI25XfDvA8Zerf0QXDqp8kpUkvFC7ql8pEzwMQa0qgurVoedAqb2baqxTZXaVN9tqjKZ-GiKCXZLDH_R_7i-ADkveWw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2686903498</pqid></control><display><type>article</type><title>Boundedness of vector-valued Calderón-Zygmund operators on non-homogeneous metric measure spaces</title><source>Springer Nature - Complete Springer Journals</source><creator>Han, Yaoyao</creator><creatorcontrib>Han, Yaoyao</creatorcontrib><description>Let
(
X
,
d
,
μ
)
be a non-homogeneous metric measure space and satisfies non-atomic condition that
μ
(
{
x
}
)
=
0
for all
x
∈
X
.
B
1
and
B
2
are Banach spaces. In this paper, we show that the boundedness of the vector-valued Calderón-Zygmund operator
T
→
from
L
2
(
X
,
B
1
)
to
L
2
(
X
,
B
2
)
is equivalent to
T
→
from
L
p
(
X
,
B
1
)
to
L
p
(
X
,
B
2
)
for
p
∈
(
1
,
∞
)
, and from
L
1
(
X
,
B
1
)
to
L
1
,
∞
(
X
,
B
2
)
. As an application, we prove that if
T
→
is bounded from
L
2
(
X
,
B
1
)
to
L
2
(
X
,
B
2
)
, then its maximal operator is bounded from
L
p
(
X
,
B
1
)
to
L
p
(
X
,
B
2
)
for
p
∈
(
1
,
∞
)
and from
L
1
(
X
,
B
1
)
to
L
1
,
∞
(
X
,
B
2
)
.</description><identifier>ISSN: 1662-9981</identifier><identifier>EISSN: 1662-999X</identifier><identifier>DOI: 10.1007/s11868-022-00468-5</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Banach spaces ; Functional Analysis ; Mathematics ; Mathematics and Statistics ; Operator Theory ; Partial Differential Equations</subject><ispartof>Journal of pseudo-differential operators and applications, 2022-09, Vol.13 (3), Article 36</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022.</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c249t-1faf613fe87f01137c894917cffb1801fd5ee7af534581673198d600ec14ac583</citedby><cites>FETCH-LOGICAL-c249t-1faf613fe87f01137c894917cffb1801fd5ee7af534581673198d600ec14ac583</cites><orcidid>0000-0003-4076-1026</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11868-022-00468-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11868-022-00468-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,778,782,27911,27912,41475,42544,51306</link.rule.ids></links><search><creatorcontrib>Han, Yaoyao</creatorcontrib><title>Boundedness of vector-valued Calderón-Zygmund operators on non-homogeneous metric measure spaces</title><title>Journal of pseudo-differential operators and applications</title><addtitle>J. Pseudo-Differ. Oper. Appl</addtitle><description>Let
(
X
,
d
,
μ
)
be a non-homogeneous metric measure space and satisfies non-atomic condition that
μ
(
{
x
}
)
=
0
for all
x
∈
X
.
B
1
and
B
2
are Banach spaces. In this paper, we show that the boundedness of the vector-valued Calderón-Zygmund operator
T
→
from
L
2
(
X
,
B
1
)
to
L
2
(
X
,
B
2
)
is equivalent to
T
→
from
L
p
(
X
,
B
1
)
to
L
p
(
X
,
B
2
)
for
p
∈
(
1
,
∞
)
, and from
L
1
(
X
,
B
1
)
to
L
1
,
∞
(
X
,
B
2
)
. As an application, we prove that if
T
→
is bounded from
L
2
(
X
,
B
1
)
to
L
2
(
X
,
B
2
)
, then its maximal operator is bounded from
L
p
(
X
,
B
1
)
to
L
p
(
X
,
B
2
)
for
p
∈
(
1
,
∞
)
and from
L
1
(
X
,
B
1
)
to
L
1
,
∞
(
X
,
B
2
)
.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Banach spaces</subject><subject>Functional Analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operator Theory</subject><subject>Partial Differential Equations</subject><issn>1662-9981</issn><issn>1662-999X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KAzEUhYMoWGpfwNWA62juZH6SpRb_oOBGQdyEmLmpLZ1kTGYKfS4fwRczdUR33s25i--cezmEnAI7B8bqiwggKkFZnlPGirSVB2QCVZVTKeXz4e8u4JjMYlyzNFxyAD4h-soPrsHGYYyZt9kWTe8D3erNgE0215sGw-eHoy-7ZZvAzHcYdCIS7DLnHX3zrV-iQz_ErMU-rEwSHYeAWey0wXhCjqzeRJz96JQ83Vw_zu_o4uH2fn65oCYvZE_BalsBtyhqy9JrtRGykFAba19BMLBNiVhrW_KiFFDVHKRoKsbQQKFNKfiUnI25XfDvA8Zerf0QXDqp8kpUkvFC7ql8pEzwMQa0qgurVoedAqb2baqxTZXaVN9tqjKZ-GiKCXZLDH_R_7i-ADkveWw</recordid><startdate>20220901</startdate><enddate>20220901</enddate><creator>Han, Yaoyao</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-4076-1026</orcidid></search><sort><creationdate>20220901</creationdate><title>Boundedness of vector-valued Calderón-Zygmund operators on non-homogeneous metric measure spaces</title><author>Han, Yaoyao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c249t-1faf613fe87f01137c894917cffb1801fd5ee7af534581673198d600ec14ac583</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Banach spaces</topic><topic>Functional Analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operator Theory</topic><topic>Partial Differential Equations</topic><toplevel>online_resources</toplevel><creatorcontrib>Han, Yaoyao</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of pseudo-differential operators and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Han, Yaoyao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Boundedness of vector-valued Calderón-Zygmund operators on non-homogeneous metric measure spaces</atitle><jtitle>Journal of pseudo-differential operators and applications</jtitle><stitle>J. Pseudo-Differ. Oper. Appl</stitle><date>2022-09-01</date><risdate>2022</risdate><volume>13</volume><issue>3</issue><artnum>36</artnum><issn>1662-9981</issn><eissn>1662-999X</eissn><abstract>Let
(
X
,
d
,
μ
)
be a non-homogeneous metric measure space and satisfies non-atomic condition that
μ
(
{
x
}
)
=
0
for all
x
∈
X
.
B
1
and
B
2
are Banach spaces. In this paper, we show that the boundedness of the vector-valued Calderón-Zygmund operator
T
→
from
L
2
(
X
,
B
1
)
to
L
2
(
X
,
B
2
)
is equivalent to
T
→
from
L
p
(
X
,
B
1
)
to
L
p
(
X
,
B
2
)
for
p
∈
(
1
,
∞
)
, and from
L
1
(
X
,
B
1
)
to
L
1
,
∞
(
X
,
B
2
)
. As an application, we prove that if
T
→
is bounded from
L
2
(
X
,
B
1
)
to
L
2
(
X
,
B
2
)
, then its maximal operator is bounded from
L
p
(
X
,
B
1
)
to
L
p
(
X
,
B
2
)
for
p
∈
(
1
,
∞
)
and from
L
1
(
X
,
B
1
)
to
L
1
,
∞
(
X
,
B
2
)
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s11868-022-00468-5</doi><orcidid>https://orcid.org/0000-0003-4076-1026</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1662-9981 |
| ispartof | Journal of pseudo-differential operators and applications, 2022-09, Vol.13 (3), Article 36 |
| issn | 1662-9981 1662-999X |
| language | eng |
| recordid | cdi_proquest_journals_2686903498 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Analysis Applications of Mathematics Banach spaces Functional Analysis Mathematics Mathematics and Statistics Operator Theory Partial Differential Equations |
| title | Boundedness of vector-valued Calderón-Zygmund operators on non-homogeneous metric measure spaces |
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