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- David Cruz-Uribe, Alberto Fiorenza
- 2010

We consider the relationship in the variable Lebesgue space L p(·)(Ω) between convergence in norm, convergence in modular, and convergence in measure, for both bounded and unbounded exponent functions.

An optimal decomposition formula for the norm in the Orlicz space L(log L) is given. New proofs of some results involving L(log L) spaces are given and the decomposition is applied to apriori estimates for elliptic partial differential equations with the right-hand side in Zygmund classes. 2000 Mathematics Subject Classification: 46E35, 46E39, 35J05.

- Claudia Capone, Alberto Fiorenza, ANDMIROSLAV KRBEC
- 2006

Yano’s extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive operator T acting continuously in Lp for p close to 1 and/or taking L∞ into Lp as p→ 1+ and/or p→∞ with norms blowing up at speed (p− 1)−α and/or pβ, α,β > 0. Here we give answers in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces to what happens… (More)

We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents… (More)

we will consider the case, with respect to the measure μ and the value of q, where un converges to a function u that does not satisfy (1.1). Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli, via Monteoliveto 3, 80134 Napoli, Italia, and Istituto per le Applicazioni del Calcolo “Mauro Picone” Sezione di Napoli, Consiglio… (More)

We study the links between additive and multiplicative arithmetical functions, say f , and their square-free supported counterparts, i.e. μf (here μ is the square-free numbers characteristic function), regarding the (upper bound) estimate of their symmetry around x in almost all short intervals [x− h, x + h].

- ANNA MARIA D’ARISTOTILE, Alberto Fiorenza
- 2006

We consider sets of inequalities in Real Analysis and construct a topology such that inequalities usually called “limit cases” of certain sequences of inequalities are in fact limits in the precise topological sense of such sequences. To show the generality of the results, several examples are given for the notions introduced, and three main examples are… (More)

In this paper we prove higher integrability results for vector fields B,E, (B,E) ∈ L2− (Ω, R) × L2−ε(Ω, R), ε small, such that div B = 0, curl E = 0 satisfying a “reverse” inequality of the type |B| + |E| ≤ ( K + 1 K ) 〈B,E〉+ |F | with K ≥ 1 and F ∈ L(Ω, R), r > 2 − ε. Applications to the theory of quasiconformal mappings and partial differential equations… (More)

- Alberto Fiorenza, Anna Mercaldo, Jean-Michel Rakotoson
- Appl. Math. Lett.
- 2001

we extend the results. of [I-5] on the uniqueness of solutions of parabolic equations. Our results give also some regularity results which complete the existence results made in [6-81. @ 2001 Elsevier Science Ltd. All rights reserved. Keywords-Parabolic equations, Radon measures, Hodge decomposition, Uniqueness, Regularity.

- Ralph Chill, Alberto Fiorenza, RALPH CHILL, Alberto Fiorenza
- 2017

We prove two extrapolation results for singular integral operators with operator-valued kernels and we apply these results in order to obtain the following extrapolation of Lp-maximal regularity: if an autonomous Cauchy problem on a Banach space has Lp-maximal regularity for some p ∈ (1,∞), then it has Ew-maximal regularity for every rearrangement-invariant… (More)