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Some Spaces of Harmonic Functions in the Unit Ball of ℝn
We introduce the Banach spaces h ∞ ( ϕ ) , h 0 ( ϕ ) and h 1 ( ψ ) functions harmonic in the unit ball B ⊂ ℝ n . These spaces depend on weight functions ϕ, ψ . We prove that if ϕ and ψ form a normal pair, then h 1 ( ψ ) * ∼ h ∞ ( ϕ ) and h 0 ( ϕ )* ∼ h 1 ( ψ ).
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| Published in: | Lobachevskii journal of mathematics 2019-08, Vol.40 (8), p.1132-1136 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c853-7121f07a740d8c2dfdc548468db601744e9d5b6944fd39adcdf5822ff6b6d9233 |
| container_end_page | 1136 |
| container_issue | 8 |
| container_start_page | 1132 |
| container_title | Lobachevskii journal of mathematics |
| container_volume | 40 |
| creator | Petrosyan, A. I. |
| description | We introduce the Banach spaces
h
∞
(
ϕ
)
, h
0
(
ϕ
) and
h
1
(
ψ
) functions harmonic in the unit ball
B
⊂ ℝ
n
. These spaces depend on weight functions
ϕ, ψ
. We prove that if
ϕ
and
ψ
form a normal pair, then
h
1
(
ψ
)
*
∼
h
∞
(
ϕ
) and
h
0
(
ϕ
)*
∼ h
1
(
ψ
). |
| doi_str_mv | 10.1134/S1995080219080213 |
| format | article |
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h
∞
(
ϕ
)
, h
0
(
ϕ
) and
h
1
(
ψ
) functions harmonic in the unit ball
B
⊂ ℝ
n
. These spaces depend on weight functions
ϕ, ψ
. We prove that if
ϕ
and
ψ
form a normal pair, then
h
1
(
ψ
)
*
∼
h
∞
(
ϕ
) and
h
0
(
ϕ
)*
∼ h
1
(
ψ
).</description><identifier>ISSN: 1995-0802</identifier><identifier>EISSN: 1818-9962</identifier><identifier>DOI: 10.1134/S1995080219080213</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Algebra ; Analysis ; Geometry ; Mathematical Logic and Foundations ; Mathematics ; Mathematics and Statistics ; Probability Theory and Stochastic Processes</subject><ispartof>Lobachevskii journal of mathematics, 2019-08, Vol.40 (8), p.1132-1136</ispartof><rights>Pleiades Publishing, Ltd. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c853-7121f07a740d8c2dfdc548468db601744e9d5b6944fd39adcdf5822ff6b6d9233</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Petrosyan, A. I.</creatorcontrib><title>Some Spaces of Harmonic Functions in the Unit Ball of ℝn</title><title>Lobachevskii journal of mathematics</title><addtitle>Lobachevskii J Math</addtitle><description>We introduce the Banach spaces
h
∞
(
ϕ
)
, h
0
(
ϕ
) and
h
1
(
ψ
) functions harmonic in the unit ball
B
⊂ ℝ
n
. These spaces depend on weight functions
ϕ, ψ
. We prove that if
ϕ
and
ψ
form a normal pair, then
h
1
(
ψ
)
*
∼
h
∞
(
ϕ
) and
h
0
(
ϕ
)*
∼ h
1
(
ψ
).</description><subject>Algebra</subject><subject>Analysis</subject><subject>Geometry</subject><subject>Mathematical Logic and Foundations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Probability Theory and Stochastic Processes</subject><issn>1995-0802</issn><issn>1818-9962</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9j01OwzAQhS0EEqVwAHa-QMDjOI7NDiraIlVikbKOHP9AqsSu7HTBnmtwOU5CQtkhsZkZ6b1v9B5C10BuAHJ2W4GUBRGEgvyZ-QmagQCRScnp6XiPcjYp5-gipR0hlHLOZ-iuCr3F1V5pm3BweK1iH3yr8fLg9dAGn3Dr8fBm8YtvB_ygum6yfX18-kt05lSX7NXvnqPt8nG7WGeb59XT4n6TaVHkWQkUHClVyYgRmhpndMEE48I0nEDJmJWmaLhkzJlcKqONKwSlzvGGG0nzfI7g-FbHkFK0rt7HtlfxvQZST93rP91Hhh6ZNHr9q431LhyiH1P-A30DzC1abg</recordid><startdate>201908</startdate><enddate>201908</enddate><creator>Petrosyan, A. I.</creator><general>Pleiades Publishing</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201908</creationdate><title>Some Spaces of Harmonic Functions in the Unit Ball of ℝn</title><author>Petrosyan, A. I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c853-7121f07a740d8c2dfdc548468db601744e9d5b6944fd39adcdf5822ff6b6d9233</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Geometry</topic><topic>Mathematical Logic and Foundations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Probability Theory and Stochastic Processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Petrosyan, A. I.</creatorcontrib><collection>CrossRef</collection><jtitle>Lobachevskii journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Petrosyan, A. I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some Spaces of Harmonic Functions in the Unit Ball of ℝn</atitle><jtitle>Lobachevskii journal of mathematics</jtitle><stitle>Lobachevskii J Math</stitle><date>2019-08</date><risdate>2019</risdate><volume>40</volume><issue>8</issue><spage>1132</spage><epage>1136</epage><pages>1132-1136</pages><issn>1995-0802</issn><eissn>1818-9962</eissn><abstract>We introduce the Banach spaces
h
∞
(
ϕ
)
, h
0
(
ϕ
) and
h
1
(
ψ
) functions harmonic in the unit ball
B
⊂ ℝ
n
. These spaces depend on weight functions
ϕ, ψ
. We prove that if
ϕ
and
ψ
form a normal pair, then
h
1
(
ψ
)
*
∼
h
∞
(
ϕ
) and
h
0
(
ϕ
)*
∼ h
1
(
ψ
).</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1995080219080213</doi><tpages>5</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1995-0802 |
| ispartof | Lobachevskii journal of mathematics, 2019-08, Vol.40 (8), p.1132-1136 |
| issn | 1995-0802 1818-9962 |
| language | eng |
| recordid | cdi_crossref_primary_10_1134_S1995080219080213 |
| source | Springer Nature |
| subjects | Algebra Analysis Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes |
| title | Some Spaces of Harmonic Functions in the Unit Ball of ℝn |
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