Alberto Fiorenza

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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 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 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)
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.
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)