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New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space
Let ψ and φ be analytic functions on the open unit disk with φ( ) ⊆ . We give new characterizations of the bounded and compact weighted composition operators W ψ,ϕ from the Hardy spaces H p , 1 ≤ p ≤ ∞, the Bloch space B , the weighted Bergman spaces A α p , α > − 1,1 ≤ p < ∞, and the Dirichle...
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| Published in: | Central European journal of mathematics 2013-01, Vol.11 (1), p.55-73 |
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| Language: | English |
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| container_end_page | 73 |
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| container_title | Central European journal of mathematics |
| container_volume | 11 |
| creator | Colonna, Flavia |
| description | Let ψ and φ be analytic functions on the open unit disk
with φ(
) ⊆
. We give new characterizations of the bounded and compact weighted composition operators
W
ψ,ϕ
from the Hardy spaces
H
p
, 1 ≤
p
≤ ∞, the Bloch space
B
, the weighted Bergman spaces
A
α
p
,
α
> − 1,1 ≤
p
< ∞, and the Dirichlet space
to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of
W
ψ,ϕ
f
for suitable collections of functions
f
in the respective spaces. We also obtain characterizations of boundedness for
H
1
as well as of compactness for
H
p
, 1 ≤
p
< ∞, and
purely in terms of the symbols
ψ
and
φ
. |
| doi_str_mv | 10.2478/s11533-012-0097-4 |
| format | article |
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with φ(
) ⊆
. We give new characterizations of the bounded and compact weighted composition operators
W
ψ,ϕ
from the Hardy spaces
H
p
, 1 ≤
p
≤ ∞, the Bloch space
B
, the weighted Bergman spaces
A
α
p
,
α
> − 1,1 ≤
p
< ∞, and the Dirichlet space
to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of
W
ψ,ϕ
f
for suitable collections of functions
f
in the respective spaces. We also obtain characterizations of boundedness for
H
1
as well as of compactness for
H
p
, 1 ≤
p
< ∞, and
purely in terms of the symbols
ψ
and
φ
.</description><identifier>ISSN: 1895-1074</identifier><identifier>EISSN: 1644-3616</identifier><identifier>EISSN: 2391-5455</identifier><identifier>DOI: 10.2478/s11533-012-0097-4</identifier><language>eng</language><publisher>Heidelberg: SP Versita</publisher><subject>30H10 ; 30H20 ; 30H30 ; 47B38 ; Algebra ; Analytic functions ; Bloch space ; Composition ; Dirichlet problem ; Dirichlet space ; Geometry ; Hardy space ; Lie Groups ; Mathematics ; Mathematics and Statistics ; Norms ; Number Theory ; Operators (mathematics) ; Probability Theory and Stochastic Processes ; Research Article ; Topological Groups ; Weighted Bergman space ; Weighted composition operators</subject><ispartof>Central European journal of mathematics, 2013-01, Vol.11 (1), p.55-73</ispartof><rights>Versita Warsaw and Springer-Verlag Wien 2012</rights><rights>2013. This work is published under http://creativecommons.org/licenses/by-nc-nd/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c437t-61d2de78ef12bae7726f514a24c2bd19b7df1d9327a515bc6a7ec6641a0b3dc23</citedby><cites>FETCH-LOGICAL-c437t-61d2de78ef12bae7726f514a24c2bd19b7df1d9327a515bc6a7ec6641a0b3dc23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.degruyter.com/document/doi/10.2478/s11533-012-0097-4/pdf$$EPDF$$P50$$Gwalterdegruyter$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2545266817?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,25730,27900,27901,36988,44565,67128,68912</link.rule.ids></links><search><creatorcontrib>Colonna, Flavia</creatorcontrib><title>New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space</title><title>Central European journal of mathematics</title><addtitle>centr.eur.j.math</addtitle><description>Let ψ and φ be analytic functions on the open unit disk
with φ(
) ⊆
. We give new characterizations of the bounded and compact weighted composition operators
W
ψ,ϕ
from the Hardy spaces
H
p
, 1 ≤
p
≤ ∞, the Bloch space
B
, the weighted Bergman spaces
A
α
p
,
α
> − 1,1 ≤
p
< ∞, and the Dirichlet space
to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of
W
ψ,ϕ
f
for suitable collections of functions
f
in the respective spaces. We also obtain characterizations of boundedness for
H
1
as well as of compactness for
H
p
, 1 ≤
p
< ∞, and
purely in terms of the symbols
ψ
and
φ
.</description><subject>30H10</subject><subject>30H20</subject><subject>30H30</subject><subject>47B38</subject><subject>Algebra</subject><subject>Analytic functions</subject><subject>Bloch space</subject><subject>Composition</subject><subject>Dirichlet problem</subject><subject>Dirichlet space</subject><subject>Geometry</subject><subject>Hardy space</subject><subject>Lie Groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Norms</subject><subject>Number Theory</subject><subject>Operators (mathematics)</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Research Article</subject><subject>Topological Groups</subject><subject>Weighted Bergman space</subject><subject>Weighted composition operators</subject><issn>1895-1074</issn><issn>1644-3616</issn><issn>2391-5455</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNqNkUuLFDEUhQtRcBz9Ae4CrktzU3nVRtDBx8CgG12HVHJTnba7UiZpmvn3ZqZEVwOzys3hnu-EnK57DfQt40q_KwBiGHoKrKd0VD1_0l2A5LwfJMinbdaj6IEq_rx7UcqeUkY1wEX36xueicuxYo6WhJTJlE6LR79gKcQunrh0XK2r9_cUyBnjvKu46anEGtNC0orZ1pQLOdp1jctM4lITqTskHw_J7UhpCHzZPQv2UPDV3_Oy-_n504-rr_3N9y_XVx9uescHVXsJnnlUGgOwyaJSTAYB3DLu2ORhnJQP4MeBKStATE5ahU5KDpZOg3dsuOyuN65Pdm_WHI8235pko7kXUp6NzTW6A5qgtGB6dNpp5IpZq-WEk5SoA6NeQWO92VhrTr9PWKrZp1Ne2vMNE1wwKTWotgXblsuplIzhXypQc9eP2foxrR9z14_hzfN-85ztof2-xzmfbtvwP-BBLzRBNADbAKWFLfOjnMMf8D6oGw</recordid><startdate>20130101</startdate><enddate>20130101</enddate><creator>Colonna, Flavia</creator><general>SP Versita</general><general>Versita</general><general>De Gruyter Poland</general><general>De Gruyter</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7XB</scope><scope>88I</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>M2P</scope><scope>P62</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PIMPY</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>Q9U</scope><scope>DOA</scope></search><sort><creationdate>20130101</creationdate><title>New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space</title><author>Colonna, Flavia</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c437t-61d2de78ef12bae7726f514a24c2bd19b7df1d9327a515bc6a7ec6641a0b3dc23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>30H10</topic><topic>30H20</topic><topic>30H30</topic><topic>47B38</topic><topic>Algebra</topic><topic>Analytic functions</topic><topic>Bloch space</topic><topic>Composition</topic><topic>Dirichlet problem</topic><topic>Dirichlet space</topic><topic>Geometry</topic><topic>Hardy space</topic><topic>Lie Groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Norms</topic><topic>Number Theory</topic><topic>Operators (mathematics)</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Research Article</topic><topic>Topological Groups</topic><topic>Weighted Bergman space</topic><topic>Weighted composition operators</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Colonna, Flavia</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Database (1962 - 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with φ(
) ⊆
. We give new characterizations of the bounded and compact weighted composition operators
W
ψ,ϕ
from the Hardy spaces
H
p
, 1 ≤
p
≤ ∞, the Bloch space
B
, the weighted Bergman spaces
A
α
p
,
α
> − 1,1 ≤
p
< ∞, and the Dirichlet space
to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of
W
ψ,ϕ
f
for suitable collections of functions
f
in the respective spaces. We also obtain characterizations of boundedness for
H
1
as well as of compactness for
H
p
, 1 ≤
p
< ∞, and
purely in terms of the symbols
ψ
and
φ
.</abstract><cop>Heidelberg</cop><pub>SP Versita</pub><doi>10.2478/s11533-012-0097-4</doi><tpages>19</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1895-1074 |
| ispartof | Central European journal of mathematics, 2013-01, Vol.11 (1), p.55-73 |
| issn | 1895-1074 1644-3616 2391-5455 |
| language | eng |
| recordid | cdi_doaj_primary_oai_doaj_org_article_f785289c8c8e472aa86beb66e8f20d71 |
| source | Publicly Available Content Database; Walter De Gruyter: Open Access Journals |
| subjects | 30H10 30H20 30H30 47B38 Algebra Analytic functions Bloch space Composition Dirichlet problem Dirichlet space Geometry Hardy space Lie Groups Mathematics Mathematics and Statistics Norms Number Theory Operators (mathematics) Probability Theory and Stochastic Processes Research Article Topological Groups Weighted Bergman space Weighted composition operators |
| title | New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space |
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