作者：
Fiorenza, A.Gogatishvili, A.Nekvinda, A.Rakotoson, J. M.Univ Napoli Federico II
Dipartimento Architettura Via Monteoliveto 2 I-80134 Naples Italy CNR
Ist Applicaz Calcolo Mauro Picone Sez Napoli Via Pietro Castellino 111 I-80131 Naples Italy Czech Acad Sci
Inst Math Zitna 25 Prague 11567 1 Czech Republic Czech Tech Univ
Fac Civil Engn Math Inst Thakurova 7 Prague 16629 6 Czech Republic Univ Poitiers
Lab Math & Applicat UMR CNRS 7348 SP2MI Bat H3Bd Marie & Pierre CurieTeleport 2 F-86962 Futuroscope France
Given the Lebesgue space with variable exponent L-s(.)(Omega) whose norm is denoted by parallel *** to(s(.)), we show the following equivalence: lim(vertical bar E vertical bar -> 0) parallel to chi(E)parallel to(s...
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Given the Lebesgue space with variable exponent L-s(.)(Omega) whose norm is denoted by parallel *** to(s(.)), we show the following equivalence: lim(vertical bar E vertical bar -> 0) parallel to chi(E)parallel to(s(.)) = 0 if and only if lim(p ->+infinity) 1/p [f(Omega)s(x)(p)dx](1/p) = 0, where chi(E) is the characteristic function of the measurable set E and vertical bar E vertical bar its Lebesgue measure. We apply such results to characterize characterize compactness of some inclusions. (C) 2021 Elsevier Masson SAS. All rights reserved.
Some new refined versions of the Jensen, Minkowski, and Hardy inequalities are stated and proved. In particular, these results both generalize and unify several results of this type. Some results are also new for the ...
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Some new refined versions of the Jensen, Minkowski, and Hardy inequalities are stated and proved. In particular, these results both generalize and unify several results of this type. Some results are also new for the classical situation.
We prove that the class of banachfunction lattices in which all relatively weakly compact sets are equi-integrable sets (i.e. spaces satisfying the Dunford-Pettis criterion) coincides with the class of 1-disjointly h...
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We prove that the class of banachfunction lattices in which all relatively weakly compact sets are equi-integrable sets (i.e. spaces satisfying the Dunford-Pettis criterion) coincides with the class of 1-disjointly homogeneous banach lattices. New examples of such spaces are provided. Furthermore, it is shown that Dunford-Pettis criterion is equivalent to de la Vallee Poussin criterion in all rearrangement invariant spaces on the interval. Finally, the results are applied to characterize weakly compact pointwise multipliers between banachfunction lattices.
We prove that if 1 ]0, infinity[ is continuous, nondecreasing, and satisfies the Delta(2) condition near the origin, then (delta) over bar(epsilon) := [sup(0<zeta<epsilon) delta(zeta)(1/p-zeta)](p-epsilon) appro...
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We prove that if 1 < p < infinity and delta :]0,p - 1]->]0, infinity[ is continuous, nondecreasing, and satisfies the Delta(2) condition near the origin, then (delta) over bar(epsilon) := [sup(0function 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.
We prove new inequalities for the spectral radius, essential spectral radius, operator norm, measure of noncompactness and numerical radius of Hadamard weighted geometric mean of (infinite or finite) nonnegative matri...
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We prove new inequalities for the spectral radius, essential spectral radius, operator norm, measure of noncompactness and numerical radius of Hadamard weighted geometric mean of (infinite or finite) nonnegative matrices that define positive operators on banach sequence spaces. Some of these inequalities complement the known inequalities and some of them refine known inequalities. Several inequalities appear to be new even in the finite dimensional case.
作者：
Fiorenza, AlbertoGiannetti, FlaviaUniv Napoli
Dipartimento Architettura Via Monteoliveto 3 I-80134 Naples Italy CNR
Sez Napoli Ist Applicaz Calcolo Mauro Picone Via Pietro Castellino 111 I-80131 Naples Italy Univ Napoli
Dipartimento Matemat & Applicaz R Caccioppoli Via Cintia I-80126 Naples Italy
We introduce a notion of modular with a corresponding modular function space in order to build a modular capacity theory. We give two different definitions of capacity, one of them of variational type, the other one t...
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We introduce a notion of modular with a corresponding modular function space in order to build a modular capacity theory. We give two different definitions of capacity, one of them of variational type, the other one through either the modular of the test functions, or the modular of their gradients. We study, in both cases, the removability of sets of zero capacity in fairly general abstract Sobolev spaces with zero boundary values. As a key tool, we establish a modular Poincare inequality. With the notion of modular function space in hands, we find a way to introduce a banachfunction space, which allows to compare the zero capacity sets with respect to both notions. Thanks to this comparison, we characterize the compact sets of zero variational type capacity as removable sets. The paper is enriched with several examples, extending and unifying many results already known in literature in the settings of Musielak-Orlicz-Sobolev spaces, Lorentz-Sobolev spaces, variable exponent Sobolev spaces.
In this paper we continue the investigation of topological properties of the unbounded norm (un-)topology in normed lattices. We characterize separability and second countability of the un-topology in terms of propert...
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In this paper we continue the investigation of topological properties of the unbounded norm (un-)topology in normed lattices. We characterize separability and second countability of the un-topology in terms of properties of the underlying normed lattice. We apply our results to prove that an order continuous banachfunction space X over a semi-finite measure space is separable if and only if it has a s-finite carrier and is separable with respect to the topology of local convergence in measure. We also address the question when a normed lattice is a normal space with respect to the un-topology.
The study of the banach-Saks property in banachspaces has a long and illustrious history. Of late, motivated by applications in financial mathematics, interest has arisen in the banach-Saks type properties with respe...
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The study of the banach-Saks property in banachspaces has a long and illustrious history. Of late, motivated by applications in financial mathematics, interest has arisen in the banach-Saks type properties with respect to order convergence. This paper presents a study of order banach-Saks properties in banach function spaces, and in particular in rearrangement invariant spaces. Among the results obtained, we provide some sufficient conditions for the (weak) order banach-Saks property. We also characterize the (weak) order banach-Saks property in Orlicz spaces. It is also shown that the (weak) order banach-Saks property is equivalent to its hereditary version. (c) 2022 Elsevier Inc. All rights reserved.
We generalize the extrapolation theory of Rubio de Francia to the context of banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted estimates for the Hardy-Littlewood m...
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We generalize the extrapolation theory of Rubio de Francia to the context of banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted estimates for the Hardy-Littlewood maximal function and are stated in measure spaces and for general Muckenhoupt bases. Finally, we give several applications in analysis and partial differential equations. (c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).
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