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Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions
Let be the space of bounded and continuous functions equipped with the norm and let e j , j = 1,…, m , be a standard basis in : Given moduli of continuity ω j , j = 1,…, m , denote We obtain new sharp Kolmogorov-type inequalities for the norms of mixed fractional derivatives of functions . Some appl...
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| Published in: | Ukrainian mathematical journal 2010-10, Vol.62 (3), p.343-357 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c370t-2a3cae66cce5269f7d0a27eecf23d0cfa08412bbb4c5cd466546a5f539cfabcb3 |
| container_end_page | 357 |
| container_issue | 3 |
| container_start_page | 343 |
| container_title | Ukrainian mathematical journal |
| container_volume | 62 |
| creator | Babenko, V. F. Parfinovych, N.V. Pichugov, S. A. |
| description | Let
be the space of bounded and continuous functions
equipped with the norm
and let
e
j
,
j
= 1,…,
m
, be a standard basis in
: Given moduli of continuity ω
j
,
j
= 1,…,
m
, denote
We obtain new sharp Kolmogorov-type inequalities for the norms
of mixed fractional derivatives of functions
. Some applications of these inequalities are presented. |
| doi_str_mv | 10.1007/s11253-010-0358-y |
| format | article |
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be the space of bounded and continuous functions
equipped with the norm
and let
e
j
,
j
= 1,…,
m
, be a standard basis in
: Given moduli of continuity ω
j
,
j
= 1,…,
m
, denote
We obtain new sharp Kolmogorov-type inequalities for the norms
of mixed fractional derivatives of functions
. Some applications of these inequalities are presented.</description><identifier>ISSN: 0041-5995</identifier><identifier>EISSN: 1573-9376</identifier><identifier>DOI: 10.1007/s11253-010-0358-y</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Geometry ; Mathematics ; Mathematics and Statistics ; Statistics</subject><ispartof>Ukrainian mathematical journal, 2010-10, Vol.62 (3), p.343-357</ispartof><rights>Springer Science+Business Media, Inc. 2010</rights><rights>COPYRIGHT 2010 Springer</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c370t-2a3cae66cce5269f7d0a27eecf23d0cfa08412bbb4c5cd466546a5f539cfabcb3</citedby><cites>FETCH-LOGICAL-c370t-2a3cae66cce5269f7d0a27eecf23d0cfa08412bbb4c5cd466546a5f539cfabcb3</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>Babenko, V. F.</creatorcontrib><creatorcontrib>Parfinovych, N.V.</creatorcontrib><creatorcontrib>Pichugov, S. A.</creatorcontrib><title>Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions</title><title>Ukrainian mathematical journal</title><addtitle>Ukr Math J</addtitle><description>Let
be the space of bounded and continuous functions
equipped with the norm
and let
e
j
,
j
= 1,…,
m
, be a standard basis in
: Given moduli of continuity ω
j
,
j
= 1,…,
m
, denote
We obtain new sharp Kolmogorov-type inequalities for the norms
of mixed fractional derivatives of functions
. Some applications of these inequalities are presented.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Statistics</subject><issn>0041-5995</issn><issn>1573-9376</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kMlOwzAURS0EEqXwAez8Ay4e4gzLqmISlVgAa-M4z8VVEhc7qZS_xzSskRe2fO95ejoI3TK6YpQWd5ExLgWhjBIqZEmmM7RgshCkEkV-jhaUZozIqpKX6CrGPU1FWhYL9Pn2pcMBv_i28zsf_JEM0wGw6-F71K0bHERsfcC9D13E3mIbtBmc73WLGwjuqAd3hFPSjW166-D0ANiO_akWr9GF1W2Em797iT4e7t83T2T7-vi8WW-JEQUdCNfCaMhzY0DyvLJFQzUvAIzloqHGalpmjNd1nRlpmizPZZZraaWoUlabWizRap670y0o11s_pE3TaaBzxvdgXfpfC1mVkmdllQA2Ayb4GANYdQiu02FSjKpfp2p2qpIq9etUTYnhMxNTt99BUHs_huQi_gP9ACmvffk</recordid><startdate>20101001</startdate><enddate>20101001</enddate><creator>Babenko, V. F.</creator><creator>Parfinovych, N.V.</creator><creator>Pichugov, S. A.</creator><general>Springer US</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20101001</creationdate><title>Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions</title><author>Babenko, V. F. ; Parfinovych, N.V. ; Pichugov, S. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c370t-2a3cae66cce5269f7d0a27eecf23d0cfa08412bbb4c5cd466546a5f539cfabcb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Babenko, V. F.</creatorcontrib><creatorcontrib>Parfinovych, N.V.</creatorcontrib><creatorcontrib>Pichugov, S. A.</creatorcontrib><collection>CrossRef</collection><jtitle>Ukrainian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Babenko, V. F.</au><au>Parfinovych, N.V.</au><au>Pichugov, S. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions</atitle><jtitle>Ukrainian mathematical journal</jtitle><stitle>Ukr Math J</stitle><date>2010-10-01</date><risdate>2010</risdate><volume>62</volume><issue>3</issue><spage>343</spage><epage>357</epage><pages>343-357</pages><issn>0041-5995</issn><eissn>1573-9376</eissn><abstract>Let
be the space of bounded and continuous functions
equipped with the norm
and let
e
j
,
j
= 1,…,
m
, be a standard basis in
: Given moduli of continuity ω
j
,
j
= 1,…,
m
, denote
We obtain new sharp Kolmogorov-type inequalities for the norms
of mixed fractional derivatives of functions
. Some applications of these inequalities are presented.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s11253-010-0358-y</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0041-5995 |
| ispartof | Ukrainian mathematical journal, 2010-10, Vol.62 (3), p.343-357 |
| issn | 0041-5995 1573-9376 |
| language | eng |
| recordid | cdi_gale_infotracacademiconefile_A359852489 |
| source | Springer Nature |
| subjects | Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Statistics |
| title | Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions |
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