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On the Space L^{p(x)}(Omega) with unbounded variable exponent $p(x)$
Liu Duchao *
Lanzhou University
*Correspondence author
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Funding: 国家自然科学基金（No.10671084）
Opened online:22 December 2008
Accepted by: none
Citation: Liu Duchao .On the Space L^{p(x)}(Omega) with unbounded variable exponent $p(x)$[OL]. [22 December 2008] http://en.paper.edu.cn/en_releasepaper/content/26824
 
 
Abstract The function space L^{p(x)}(Omega) with unbounded variable exponent, which generalizing the space L^{p(x)}(Omega) with bounded variable exponent, is investigated in this paper. We have defined a norm, investigated some basic properties of it and proved that the space is a Banach function space (and also a Banach space). Some other properties of the space, such as uniform convexity and embedding have also been investigated. As we will see, the properties of L^{p(x)}(Omega) with unbounded variable exponent is more complex than the space with bounded variable exponent.
Keywords:Embedding;Uniform convex;Banach space;Banach
 
 
 

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