Grand and Small Lebesgue Spaces and Their Analogs

By Alberto Fiorenza, G. Karadzhov. 2004

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The maximal theorem for weighted grand Lebesgue spaces (2008, methodology): “3) can be easily deduced from the expression of the norm given in [6], using the rearrangement-invariance and the standard Hardy inequality: ∥∥∥ x 0 f dt ∥∥∥ (p ≤ c(p) 1”
A direct approach to the duality of grand and small Lebesgue spaces (2009, methodology): “In [8] the following much more simple equivalent expression for the norm was found: ‖f‖(q ≈ [|f |](q := ∫ 1”
On grand and small Lebesgue and Sobolev spaces and some applications to PDE's (2018, background): “At last, we may state the characterization of grand and small Lebesgue spaces given in [61]: Lp) = (L(1),L)1,∞;− (1)p (9)”
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”