Collectanea Mathematica

, Volume 65, Issue 2, pp 273–284 | Cite as

Iterated grand and small Lebesgue spaces

Article

Abstract

The norm of the grand Lebesgue spaces is defined through the supremum of Lebesgue norms, balanced by an infinitesimal factor. In this paper we consider the spaces defined by a norm with an analogous expression, where Lebesgue norms are replaced by grand Lebesgue norms. Without the use of interpolation theory, we prove an iteration-type theorem, and we establish that the new norm is again equivalent to the norm of grand Lebesgue spaces. We prove that the expression involved satisfy the axioms of Banach Function Spaces, and we find explicit values of the constants of the equivalence. Analogous results are proved for small Lebesgue spaces.

Keywords

Grand Lebesgue spaces Small Lebesgue spaces Iteration theorem  Banach Function Spaces Duality 

Mathematics Subject Classification (2000)

46E30 46B70 

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Copyright information

© Universitat de Barcelona 2013

Authors and Affiliations

  1. 1.Dipartimento di ArchitetturaUniversità degli Studi di Napoli “Federico II”NaplesItaly

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