Uniform Convexity in Variable Exponent Sobolev Spaces

被引：0

作者：

Bachar, Mostafa ^{[1
]}

Khamsi, Mohamed A. ^{[2
]}

Mendez, Osvaldo ^{[2
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

[2] Univ Texas El Paso, Dept Math Sci, 500W Univ Ave,124 Bell Hall, El Paso, TX 79968 USA

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 11期

关键词：

fixed point; Fredholm equations; modular function spaces; variable exponent spaces;

D O I：

10.3390/sym15111988

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We prove the modular convexity of the mixed norm Lp(l2) on the Sobolev space W1,p(omega) in a domain omega subset of Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx is an element of omega p(x)=infinity. In particular, the mixed Sobolev norm is uniformly convex if 1<infx is an element of omega p(x)<= supx is an element of omega p(x)<infinity and W01,p(omega) is uniformly convex.

引用

页数：11

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