Variable Lebesgue Spaces

By D. Cruz-Uribe, Alberto Fiorenza. 2013

641 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/aca85cf091c5fae9cc110662aea203b07c800aaf

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

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], [37].”
Weighted Norm Inequalities for Rough Singular Integral Operators (2017, background): “me examples of these functions are those satisfying the following log-Ho¨lder continuous property, (A.3) |p(x)− p(y)| ≤ C |log|x −y|| , |x−y| ≤ 1/2, (A.4) |p(x)− p(y)| ≤ C log(e+|x|) , |y| ≥ |x|. See [10] and [11] for more information about these spaces. Because our proofs rely on duality arguments,”
New Examples on Lavrentiev Gap Using Fractals (2019, background): “For more details we refer to the books [5, 3, 12].”
Martingale Hardy spaces with variable exponents (2014, methodology): “a quasi-normed space. Such Lebesgue spaces were introduced by Orlicz [24] in 1931 and studied by O. Kova`˘cik and J. Ra´kosn´ık [17], X. Fan and D. Zhao [9] and others. We refer to two new monograghs [3] and [7] for the recent progress on Lebesgue spaces with variable exponents and some applications”
Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, background): “ed with dilations and variable Lebesgue spaces as well as some basic conclusions of these spaces to be used in this article. For an exposition of these concepts, we refer the reader to the monographs [10, 22, 25]. We begin with recalling the notion of expansive matrices in [10]. AnisotropicVariableH”
Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces (2019, background): “2) holds true for the space X, any s ∈ (0, 1] and any θ ∈ (0,min{s, p−}) (see, for instance, [10] and [11]); similarly, (2.”
Extrapolation and weighted norm inequalities in the variable Lebesgue spaces (2014, methodology): “Throughout we will follow the conventions established in [13].”