We prove that if 1 < p< ∞ and δ:] 0 , p- 1] →] 0 , ∞[is continuous, nondecreasing, and satisfies the Δ 2 condition near the origin, then [Figure not available: see fulltext.] This result permits to clarify the assumptions on the increasing function against the Lebesgue norm in the definition of generalized grand Lebesgue spaces and to sharpen and simplify the statements of some known results concerning these spaces.
On the Factor Opposing the Lebesgue Norm in Generalized Grand Lebesgue Spaces / Fiorenza, A.; Formica, M. R.. - In: RESULTS IN MATHEMATICS. - ISSN 1422-6383. - 76:74:2(2021), pp. 1-12. [10.1007/s00025-021-01375-9]
On the Factor Opposing the Lebesgue Norm in Generalized Grand Lebesgue Spaces
Fiorenza A.;Formica M. R.
2021
Abstract
We prove that if 1 < p< ∞ and δ:] 0 , p- 1] →] 0 , ∞[is continuous, nondecreasing, and satisfies the Δ 2 condition near the origin, then [Figure not available: see fulltext.] This result permits to clarify the assumptions on the increasing function against the Lebesgue norm in the definition of generalized grand Lebesgue spaces and to sharpen and simplify the statements of some known results concerning these spaces.File in questo prodotto:
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