o–O structure of some rearrangement invariant Banach function spaces

Ascione, Giacomo; Manzo, Gianluigi

doi:10.1007/s41808-020-00051-3

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Cited by 3 publications

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“…is the "little o "to BM O(Q 0 ) (for the theory of o-O spaces see [22], [23], [6]). Using the fact that cl…”

Section: The Unit Ball Ofmentioning

confidence: 99%

Preduals and double preduals of some Banach spaces

D'Onofrio¹,

Manzo²,

Sbordone³

et al. 2020

Preprint

Self Cite

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In this paper we study ways to establish when a Banach space can be identified as the dual or the double dual of another Banach space.To obtain these results, we relate these spaces with other, concrete Banach spaces -tipically ℓ 1 and ℓ ∞ -and show that under suitable assumptions we can transfer properties of these spaces to the space we consider. In particular, we show how these results can be used to obtain in a simple way interesting results about spaces such as BM O and BV .

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“…is the "little o "to BM O(Q 0 ) (for the theory of o-O spaces see [22], [23], [6]). Using the fact that cl…”

Section: The Unit Ball Ofmentioning

confidence: 99%

Preduals and double preduals of some Banach spaces

D'Onofrio¹,

Manzo²,

Sbordone³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Regularity results for solutions to elliptic obstacle problems in limit cases

Farroni,

Manzo

2024

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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We prove the Lewy–Stampacchia’s inequality for elliptic variational inequalities with obstacle involving Leray–Lions type operator whose simpler model case is given by the following $$\begin{aligned} u \in W^{1,N}_0(\Omega )\mapsto -\Delta _N u-\text {div}\left( B (x) |u|^{N-2}u \right) \end{aligned}$$ u ∈ W 0 1 , N ( Ω ) ↦ - Δ N u - div B ( x ) | u | N - 2 u where $$\Omega $$ Ω is a smooth bounded domain of $$\mathbb {R}^N$$ R N with $$N\geqslant 2$$ N ⩾ 2 , $$\Delta _N u$$ Δ N u denotes the classical N–Laplacian operator and the coefficient $$B:\Omega \rightarrow \mathbb {R}^N$$ B : Ω → R N belongs to a suitable Lorentz–Zygmund space. For this kind of obstacle problems, we also provide regularity results and amongst them we give sufficient conditions to get boundedness of solutions.

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A new norm on BLO, matters of approximability and duality

Angrisani

2024

Nonlinear Analysis

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o–O structure of some rearrangement invariant Banach function spaces

Cited by 3 publications

References 17 publications

Preduals and double preduals of some Banach spaces

Preduals and double preduals of some Banach spaces

Regularity results for solutions to elliptic obstacle problems in limit cases

A new norm on BLO, matters of approximability and duality

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