Data di Pubblicazione:
2013
Abstract:
Let 1
In this paper we consider the classical norm of the Grand Lebesgue space L^p) obtained considering a generic nonnegative measurable function ?(?). We find necessary and sufficient conditions on ? in order to get a functional equivalent to a Banach function norm, and we determine the "interesting" class Bp of functions ?, with the property that every generalized function norm is equivalent to a function norm built with ??Bp. We then define the Lp),?(?) spaces, prove some embedding results and conclude with the proof of the generalized Hardy inequality.
In this paper we consider the classical norm of the Grand Lebesgue space L^p) obtained considering a generic nonnegative measurable function ?(?). We find necessary and sufficient conditions on ? in order to get a functional equivalent to a Banach function norm, and we determine the "interesting" class Bp of functions ?, with the property that every generalized function norm is equivalent to a function norm built with ??Bp. We then define the Lp),?(?) spaces, prove some embedding results and conclude with the proof of the generalized Hardy inequality.
Tipologia CRIS:
01.01 Articolo in rivista
Keywords:
Grand Lebesgue spaces; Banach function spaces; Rearrangement-invariant spaces; Function norm; Embedding results; Hardy inequality
Elenco autori:
Capone, Claudia
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