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Variable exponents and grand Lebesgue spaces: Some optimal results [PDF]

Communications in Contemporary Mathematics, 2015
Consider p : Ω → [1, +∞[, a measurable bounded function on a bounded set Ø with decreasing rearrangement p* : [0, |Ω|] → [1, +∞[. We construct a rearrangement invariant space with variable exponent p* denoted by [Formula: see text]. According to the growth of p*, we compare this space to the Lebesgue spaces or grand Lebesgue spaces.
FIORENZA, ALBERTO, Rakotoson, Jean Michel, SBORDONE, CARLO   +2 more
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Sawyer's duality principle for grand Lebesgue spaces

Mathematische Nachrichten, 2018
AbstractThe aim of this paper is to extend Sawyer's duality principle from the cone of decreasing functions of the Lebesgue space to the cone of decreasing functions of the grand Lebesgue space and to prove the boundedness of classical Hardy operators in the grand Lebesgue spaces.
Jain, Pankaj, Singh, Arun Pal, Singh, Monika, Stepanov, Vladimir D.   +3 more
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Recent Trends in Grand Lebesgue Spaces

2017
The aim of this paper is two fold. Since their inception in 1992, we collect various generalizations of the grand Lebesgue spaces touching upon several of their aspects such as properties, duality, equivalent norms etc. Also, we prove certain new extrapolation results of the type of Rubio De Francia in the framework of fully measurable grand Lebesgue ...
Pankaj Jain, Monika Singh, Arun Pal Singh   +2 more
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Approximation in weighted generalized grand Lebesgue spaces

Colloquium Mathematicum, 2015
Summary: The direct and inverse problems of approximation theory in the subspace of weighted generalized grand Lebesgue spaces of \(2\pi \)-periodic functions with the weights satisfying Muckenhoupt's condition are investigated. Appropriate direct and inverse theorems are proved.
Israfilov, Daniyal M., Testici, Ahmet
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Riesz Fractional Integrals in Grand Lebesgue Spaces on ℝn

Fractional Calculus and Applied Analysis, 2016
We introduce conditions on the construction of grand Lebesgue spaces on R-n which imply the validity of the Sobolev theorem for the Riesz fractional integrals I-alpha and the boundedness of the maximal operator, in such spaces. We also give an inversion of the operator I-alpha by means of hypersingular integrals, within the frameworks of the introduced
Samko, Stefan, Umarkhadzhiev, Salaudin
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Boyd Indices in Generalized Grand Lebesgue Spaces and Applications

Mediterranean Journal of Mathematics, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
FORMICA, MARIA ROSARIA, GIOVA, Raffaella
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One-Sided Operators in Grand Variable Exponent Lebesgue Spaces

Zeitschrift für Analysis und ihre Anwendungen, 2018
The boundedness of one-sided integral operators in grand variable exponent Lebesgue spaces unifying grand Lebesgue spaces and variable exponent Lebesgue spaces are established. The conditions on variable exponent is weaker than the log-Hölder continuity condition.
Kokilashvili, Vakhtang, Meskhi, Alexander   +1 more
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Constraint handling technique based on Lebesgue measure for constrained multiobjective particle swarm optimization algorithm

Knowledge-Based Systems, 2021
Hui Wang
exaly  

Summability of Fourier transforms on mixed-norm Lebesgue spaces via associated Herz spaces

Analysis and Applications, 2023
Dachun Yang, Wen Yuan
exaly  

Neighborhood multi-granulation rough sets-based attribute reduction using Lebesgue and entropy measures in incomplete neighborhood decision systems

Knowledge-Based Systems, 2020
Lin Sun, Lanying Wang, Wei-Ping Ding
exaly