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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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Hardy inequality in variable exponent Lebesgue spaces

2007
We prove the Hardy inequality and a similar inequality for the dual Hardy operator for variable exponent Lebesgue spaces.
Diening, Lars, Samko, Stefan G.
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Lebesgue points in variable exponent spaces

2004
The concept of Lebesgue points in variable exponent Lebesgue and Sobolev spaces is studied. For Lebesgue spaces \(L^{p(\cdot)}(\mathbb{R}^n)\), it is proved that if \(\text{ess\,sup}_{x\in \mathbb{R}^n} p(x)
Harjulehto, Petteri, Hästö, Peter
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Interpolation inequalities for derivatives in variable exponent Lebesgue–Sobolev spaces

Nonlinear Analysis: Theory, Methods & Applications, 2008
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Zang, Aibin, Fu, Yong
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The inclusion theorems for generalized variable exponent grand Lebesgue spaces

2021
Summary: In this paper, we discuss and investigate the existence of the inclusion \(L^{p(.),\theta}(\mu) \subseteq L^{q(.),\theta}(\nu)\), where \(\mu\) and \(\nu\) are two finite measures on \((X,\Sigma) \). Moreover, we show that the generalized variable exponent grand Lebesgue space \(L^{p(.),\theta}(\Omega)\) has a potential-type approximate ...
Aydin, Ismail, Unal, Cihan
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Composition operators on variable exponent Lebesgue spaces

Analysis Mathematica
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Bajaj, D. S., Datt, G.
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Lebesgue and Sobolev Spaces with Variable Exponents

2011
Diening, Lars, Harjulehto, Petteri, Hästö, Peter, Růžička, Michael   +3 more
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On Compactness of Operators in Variable Exponent Lebesgue Spaces

2010
We give a short discussion of known statements on compactness of operators in variable exponent Lebesgue spaces L p (·)(Ω, ϱ) and show that the existence of a radial integrable decreasing dominant of the kernel of a convolution operator guarantees its compactness in the space L p (·)(Ω, ϱ) whenever the maximal operator is bounded in this space, where ...
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Variable Exponent Lebesgue and Sobolev Spaces

2021
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On the basicity of unitary system of exponents in the variable exponent Lebesgue spaces

2017
Summary: In the present work it is considered the system of functions \(a(t)e^{int} - b(t)e^{-int}\), \(n \in N\), with complex-valued coefficients \(a(\cdot);b(\cdot): [0, \pi]\rightarrow C\). Sufficient conditions on the coefficients of the system are found in order for the system to form a basis in Lebesgue spaces with variable exponent.
Bilalov, Bilal T., Huseynli, Ali A., Aleskerov, Miran I.   +2 more
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