Some Remarks on the Vector-Valued Variable Exponent Lebesgue Spaces $\ell^{q(\cdot)} (L^{p(\cdot)})
In this paper, we investigate the geometric properties of the variable mixed Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We show that, if $ 1
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creator | Ghorbanalizadeh, Arash Seraji, Reza Roohi |
description | In this paper, we investigate the geometric properties of the variable mixed
Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We
show that, if $ 1 |
doi_str_mv | 10.48550/arxiv.2401.03211 |
format | Article |
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Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We
show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)}
(L^{p(\cdot)})$ is strictly and uniformly convex. We also prove that when $
1\le q_-,p_-,q_+,p_+<\infty, $ the convergence in norm implies the convergence
in measure, and under some conditions on exponents, the approximation identity
holds in the space $ \ell^1(L^{\frac{p(\cdot)}{q(\cdot)}}) $.</description><identifier>DOI: 10.48550/arxiv.2401.03211</identifier><language>eng</language><subject>Mathematics - Functional Analysis</subject><creationdate>2024-01</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2401.03211$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2401.03211$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Ghorbanalizadeh, Arash</creatorcontrib><creatorcontrib>Seraji, Reza Roohi</creatorcontrib><title>Some Remarks on the Vector-Valued Variable Exponent Lebesgue Spaces $\ell^{q(\cdot)} (L^{p(\cdot)})</title><description>In this paper, we investigate the geometric properties of the variable mixed
Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We
show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)}
(L^{p(\cdot)})$ is strictly and uniformly convex. We also prove that when $
1\le q_-,p_-,q_+,p_+<\infty, $ the convergence in norm implies the convergence
in measure, and under some conditions on exponents, the approximation identity
holds in the space $ \ell^1(L^{\frac{p(\cdot)}{q(\cdot)}}) $.</description><subject>Mathematics - Functional Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNo1z0FLw0AUBOC9eJDqD_DkHjy0h8R92SabHKVULQQEW3IqDW9332owTeImlUrxv1urnoaBYeBj7ApEOE3jWNyi31cfYTQVEAoZAZwzs2y3xJ9pi_6t523Dh1fiBZmh9UGB9Y4sL9BXqGvi833XNtQMPCdN_cuO-LJDQz2_WVNdbw7v47Wx7TD54uN8c-j-2-SCnTmse7r8yxFb3c9Xs8cgf3pYzO7yABMFAYgUDVjrQGcpKesEIEY6llqlsZKkFBjhnMt0GkHmhCIrE6kTYZPj0kZyxK5_b0_KsvPVEfVZ_mjLk1Z-AzPZT3k</recordid><startdate>20240106</startdate><enddate>20240106</enddate><creator>Ghorbanalizadeh, Arash</creator><creator>Seraji, Reza Roohi</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240106</creationdate><title>Some Remarks on the Vector-Valued Variable Exponent Lebesgue Spaces $\ell^{q(\cdot)} (L^{p(\cdot)})</title><author>Ghorbanalizadeh, Arash ; Seraji, Reza Roohi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-108ac1ddf1b98e7df01aa2b53b78573e771c0fff9b8219f07ed363b60d601ad23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Functional Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Ghorbanalizadeh, Arash</creatorcontrib><creatorcontrib>Seraji, Reza Roohi</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ghorbanalizadeh, Arash</au><au>Seraji, Reza Roohi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some Remarks on the Vector-Valued Variable Exponent Lebesgue Spaces $\ell^{q(\cdot)} (L^{p(\cdot)})</atitle><date>2024-01-06</date><risdate>2024</risdate><abstract>In this paper, we investigate the geometric properties of the variable mixed
Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We
show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)}
(L^{p(\cdot)})$ is strictly and uniformly convex. We also prove that when $
1\le q_-,p_-,q_+,p_+<\infty, $ the convergence in norm implies the convergence
in measure, and under some conditions on exponents, the approximation identity
holds in the space $ \ell^1(L^{\frac{p(\cdot)}{q(\cdot)}}) $.</abstract><doi>10.48550/arxiv.2401.03211</doi><oa>free_for_read</oa></addata></record> |
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subjects | Mathematics - Functional Analysis |
title | Some Remarks on the Vector-Valued Variable Exponent Lebesgue Spaces $\ell^{q(\cdot)} (L^{p(\cdot)}) |
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