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l(q)-structure of variable exponent spaces

Hernández, Francisco L. and Ruiz, César (2012) l(q)-structure of variable exponent spaces. Journal of Mathematical Analysis and Applications, 389 (2). pp. 899-907. ISSN 0022-247X

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Abstract

It is shown that a separable variable exponent (or Nakano) function space L-p(.)(Ω) has a lattice-isomorphic copy of l(q) if and only if q is an element of Rp(.), the essential range set of the exponent function p(.). Consequently Rp(.) is a lattice-isomorphic invariant set. The values of q such that l(q) embeds isomorphically in L-p(.)(Ω) is determined. It is also proved the existence of a bounded orthogonal l(q)-projection in the space L-p(.)(Ω), for every q is an element of Rp(.)


Item Type:Article
Uncontrolled Keywords:Orlicz sequence-spaces; copies; variable exponent spaces; isomorphic l(p)-copies; bounded projections
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:15969
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Deposited On:16 Jul 2012 11:41
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