Atomic decomposition of finite signed measures on compacts of R^n

Angrisani, Francesca; Ascione, Giacomo; Manzo, Gianluigi

doi:10.5186/aasfm.2021.4645

Cited by 5 publications

(1 citation statement)

References 19 publications

(30 reference statements)

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“…and E ֒→ X then E has an isometric predual with atomic decomposition. The cases E = BM O, E = BV or E = B the space recently introduced by Bourgain-Brezis-Mironescu are included (see also [5]) . In [11] the same atomic decomposition result is proved weakening the reflexivity assumption on X.…”

Section: Atomic Decompositionsmentioning

confidence: 99%

Preduals and double preduals of some Banach spaces

D'Onofrio¹,

Manzo²,

Sbordone³

et al. 2020

Preprint

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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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Section: Atomic Decompositionsmentioning

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

Extremal Points and Sparse Optimization for Generalized Kantorovich–Rubinstein Norms

Carioni,

Iglesias,

Walter

2023

Found Comput Math

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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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Atomic decomposition of finite signed measures on compacts of R^n

Cited by 5 publications

References 19 publications

Preduals and double preduals of some Banach spaces

Preduals and double preduals of some Banach spaces

Extremal Points and Sparse Optimization for Generalized Kantorovich–Rubinstein Norms

Regularity results for solutions to elliptic obstacle problems in limit cases

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