Duality and reflexivity in grand Lebesgue spaces

By Alberto Fiorenza. 2000

291 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d82236bdff80da2b4bbf42d1e6d906d75f184f57

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Citations in the corpus

On Iwaniec-Sbordone Spaces on Sets Which May Have Infinite Measure (pp. 67-84) (2010, methodology): “Introduced in relation to problems of integrability of jacobians, these papers proved to be appropriate in various applications in partial differential equations and variational problems, they were used in the study of maximal functions, extrapolation theory etc, we refer for instance to [1, 3, 4, 7”
Maximal functions, potentials and singular integrals in grand Morrey spaces (2011, background): “Structural properties of these spaces were investigated in the papers [3–5] etc.”
Structural properties of Bilateral Grand Lebesque Spaces (2010, methodology): “The BGLS norm estimates, in particular, Orlicz norm estimates for measurable functions, e.g., for random variables are used in PDE [5]–[8], probability in Banach spaces [14], in the modern non-parametrical statistics, for example, in the so-called regression problem [15, 16].”
A Note on the Boundedness of the Hilbert Transform in Weighted Grand Lebesgue Spaces (2009, methodology): “For some properties and applications of L spaces we refer to the papers [5], [7], [2], [1].”
On small Lebesgue spaces (2005, background): “In [ 5 ] it is proved the following result, which we state here for the generalized case.”
The maximal theorem for weighted grand Lebesgue spaces (2008, background): “We conclude this section by mentioning that together with the grand Lebesgue spaces the small Lebesgue spaces L(p(0, 1) with norm ‖ · ‖(p are often considered, as associate spaces (see [1] for the definition of associate spaces, [5] for the definition of small Lebesgue spaces, and [2] and [3] for pr”
Grand and Small Lebesgue Spaces and Their Analogs (2004, methodology): “The small Lebesgue space ([10]) L consists of all measurable functions g on a finite measure space (Ω, μ) which can be represented in the form g = ∑∞ k=1 gk (convergence a.”
A direct approach to the duality of grand and small Lebesgue spaces (2009, background): “0 fgdx : f ∈M0 , ‖f‖p) ≤ 1 } They are called small Lebesgue spaces, are evidently continuously embedded in L and were first studied by the second author in [7], who found the following explicit expression of the norm (see also [4]): ‖g‖(q = inf g = ∞ ∑”
On grand and small Lebesgue and Sobolev spaces and some applications to PDE's (2018, background): “not depending on the notion of grand Lebesgue space) characterization has been found in [57] (here we exchange p and p′ for the sake of simplicity of notation):”