Variable Lebesgue Spaces: Foundations and Harmonic Analysis

By D. Cruz-Uribe, Alberto Fiorenza. 2013

778 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f62f83bf1e96a4ad19c1d5329c7296c7f1d052f9

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Citations in the corpus

Non-autonomous functionals, borderline cases and related function classes (2016, background): “At the same time, the functional V originated several studies in function spaces theory, see for instance [18, 26].”
Hölder regularity of quasiminimizers under generalized growth conditions (2017, background): “Such problems have been vigorously studied in recent years [10, 12].”
Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces (2020, background): “For more details on quasi-Banach function spaces, we refer the reader to [1,4].”
Boundedness of the Maximal and Singular Operators on Generalized Orlicz–Morrey Spaces (2013, background): “Last two decades there is an increasing interest to the study of variable exponent spaces and operators with variable parameters, in such spaces, we refer to the recent books [6], [8] and surveying papers [7], [20], [22], [38].”
Extrapolation and interpolation in generalized Orlicz spaces (2018, background): “When φ(x, t) = t we get the variable Lebesgue spaces which have been extensively studied in the past 25 years [18, 24, 33], and when φ(x, t) = t + a(x)t, p < q, we get the double phase functional recently studied in [5, 13].”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, background): “1 Muckenhoupt weights with variable exponents The classical Muckenhoupt Ap class has been generalized to the setting Ap(·) of variable exponents by [21, 29, 41] and some equivalent conditions to the boundedness of M on L w (R) has been given (see also [24, 86]).”
Commutators of multilinear Calderón-Zygmund operators with kernels of Dini's type and applications (2019, unknown): “The following generalized Hölder’s inequality holds (see [3] or [7]).”
New martingale inequalities and applications to Fourier analysis (2018, background): “If φ(x, t) := t, w(x)t, Φ(t) or t for any x ∈ R and t ∈ (0,∞), then L(R) become the classical Lebesgue spaces, the weighted Lebesgue spaces, Orlicz spaces (see, for example, [65]) or the variable Lebesgue spaces (see, for example, [14]), respectively.”
Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, background): “But the modern theory of function spaces with variable exponents was started with the articles [45] of Kováčik and Rákosnı́k and [32] of Fan and Zhao as well as [21] of Cruz-Uribe and [24] of Diening, and nowadays has been widely used in harmonic analysis (see, for example, [22, 25, 79]).”
Martingale Hardy spaces with variable exponents (2014, background): “ a quasi-normed space. Such Lebesguespaces were introduced byOrlicz [23] in 1931 and studied by O. Kov`a˘cik and J. Ra´kosn´ık [17], X. Fan and D. Zhao [12] and others. We refer to two new monograghs [4] and [9] for the recent progress on Lebesgue spaces with variable exponents and some applications”