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Multivariate Bernstein inequalities for entire functions of exponential type in Lp(Rn)(0<p<1)
In (Rahman and Schmeisser in Trans. Amer. Math. Soc. 320: 91–103, 1990 ), the authors prove that the classical Bernstein inequality also holds for 0 < p ≤ 1 . We extend their result for a differential operator induced by polynomials and find the several equivalent conditions to the Paley–Wiener t...
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| Published in: | Journal of inequalities and applications 2019-08, Vol.2019 (1) |
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| Language: | English |
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| container_title | Journal of inequalities and applications |
| container_volume | 2019 |
| creator | Bang, Ha Huy Huy, Vu Nhat Rim, Kyung Soo |
| description | In (Rahman and Schmeisser in Trans. Amer. Math. Soc. 320: 91–103,
1990
), the authors prove that the classical Bernstein inequality also holds for
0
<
p
≤
1
. We extend their result for a differential operator induced by polynomials and find the several equivalent conditions to the Paley–Wiener theorem. As applications of the results, we also derive the Paley–Wiener type theorems for some special compact sets generated by number sequences, generated by polynomial, convex compact sets, in which we show that the Bernstein type inequalities have concrete upper bounds. |
| doi_str_mv | 10.1186/s13660-019-2167-7 |
| format | article |
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1990
), the authors prove that the classical Bernstein inequality also holds for
0
<
p
≤
1
. We extend their result for a differential operator induced by polynomials and find the several equivalent conditions to the Paley–Wiener theorem. As applications of the results, we also derive the Paley–Wiener type theorems for some special compact sets generated by number sequences, generated by polynomial, convex compact sets, in which we show that the Bernstein type inequalities have concrete upper bounds.</description><identifier>EISSN: 1029-242X</identifier><identifier>DOI: 10.1186/s13660-019-2167-7</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Applications of Mathematics ; Mathematics ; Mathematics and Statistics</subject><ispartof>Journal of inequalities and applications, 2019-08, Vol.2019 (1)</ispartof><rights>The Author(s) 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0002-2196-0575</orcidid></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>Bang, Ha Huy</creatorcontrib><creatorcontrib>Huy, Vu Nhat</creatorcontrib><creatorcontrib>Rim, Kyung Soo</creatorcontrib><title>Multivariate Bernstein inequalities for entire functions of exponential type in Lp(Rn)(0<p<1)</title><title>Journal of inequalities and applications</title><addtitle>J Inequal Appl</addtitle><description>In (Rahman and Schmeisser in Trans. Amer. Math. Soc. 320: 91–103,
1990
), the authors prove that the classical Bernstein inequality also holds for
0
<
p
≤
1
. We extend their result for a differential operator induced by polynomials and find the several equivalent conditions to the Paley–Wiener theorem. As applications of the results, we also derive the Paley–Wiener type theorems for some special compact sets generated by number sequences, generated by polynomial, convex compact sets, in which we show that the Bernstein type inequalities have concrete upper bounds.</description><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1029-242X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNqdjsFqAjEURYNQqLb9AHdvqYtp8zIyo-CqpdKFbkoXbiSE8qY8GV5ikin27zuDfoGry-Vw4Cg1Rf2MuKxeEpZVpQuNq8JgVRf1SI1Rm_4tzP5eTVI6am2wXC7G6rDr2sy_LrLLBK8UJWViARY6da7lzJSg8RFIMkeCppPvzF4S-AboHLwMwLWQ_wL1FmzD7FPmM70Oa5w_qrvGtYmervugzOb96-2jSCGy_FC0R99F6ZFFbYd4e4m3fbwd4m1d3iT9Az_BUCU</recordid><startdate>20190814</startdate><enddate>20190814</enddate><creator>Bang, Ha Huy</creator><creator>Huy, Vu Nhat</creator><creator>Rim, Kyung Soo</creator><general>Springer International Publishing</general><scope>C6C</scope><orcidid>https://orcid.org/0000-0002-2196-0575</orcidid></search><sort><creationdate>20190814</creationdate><title>Multivariate Bernstein inequalities for entire functions of exponential type in Lp(Rn)(0<p<1)</title><author>Bang, Ha Huy ; Huy, Vu Nhat ; Rim, Kyung Soo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-springer_journals_10_1186_s13660_019_2167_73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bang, Ha Huy</creatorcontrib><creatorcontrib>Huy, Vu Nhat</creatorcontrib><creatorcontrib>Rim, Kyung Soo</creatorcontrib><collection>SpringerOpen</collection><jtitle>Journal of inequalities and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bang, Ha Huy</au><au>Huy, Vu Nhat</au><au>Rim, Kyung Soo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multivariate Bernstein inequalities for entire functions of exponential type in Lp(Rn)(0<p<1)</atitle><jtitle>Journal of inequalities and applications</jtitle><stitle>J Inequal Appl</stitle><date>2019-08-14</date><risdate>2019</risdate><volume>2019</volume><issue>1</issue><eissn>1029-242X</eissn><abstract>In (Rahman and Schmeisser in Trans. Amer. Math. Soc. 320: 91–103,
1990
), the authors prove that the classical Bernstein inequality also holds for
0
<
p
≤
1
. We extend their result for a differential operator induced by polynomials and find the several equivalent conditions to the Paley–Wiener theorem. As applications of the results, we also derive the Paley–Wiener type theorems for some special compact sets generated by number sequences, generated by polynomial, convex compact sets, in which we show that the Bernstein type inequalities have concrete upper bounds.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1186/s13660-019-2167-7</doi><orcidid>https://orcid.org/0000-0002-2196-0575</orcidid><oa>free_for_read</oa></addata></record> |
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| identifier | EISSN: 1029-242X |
| ispartof | Journal of inequalities and applications, 2019-08, Vol.2019 (1) |
| issn | 1029-242X |
| language | eng |
| recordid | cdi_springer_journals_10_1186_s13660_019_2167_7 |
| source | Publicly Available Content Database; Springer Nature - SpringerLink Journals - Fully Open Access |
| subjects | Analysis Applications of Mathematics Mathematics Mathematics and Statistics |
| title | Multivariate Bernstein inequalities for entire functions of exponential type in Lp(Rn)(0<p<1) |
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