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Complex interpolation of grand Lebesgue spaces
Monatshefte für Mathematik, 2017Let \(L^{p)\tau}\) denote the grand Lebesgue space on a finite measure space, \(1< p 0\), as defined in [\textit{L. Greco} et al., Manuscr. Math. 92, No. 2, 249--258 (1997; Zbl 0869.35037)]. Let \([X_0,X_1]_{\theta}\) and \([X_0,X_1]^{\theta}\) be the first and second Calderón's complex interpolation spaces for the the compatible couple of Banach ...
Hakim, Denny Ivanal +2 more
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On Quasi-Grand Lebesgue Spaces and the Hausdorff Operator
Bulletin of the Malaysian Mathematical Sciences Society, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Singh, Arun Pal +2 more
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EMBEDDING OF GRAND CENTRAL MORREY-TYPE SPACES INTO LOCAL GRAND WEIGHTED LEBESGUE SPACES
Journal of Mathematical Sciences, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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GRAND LEBESGUE SPACES ON QUASI-METRIC MEASURE SPACES OF INFINITE MEASURE
Journal of Mathematical Sciences, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V. Guliyev, S. Samko, S. Umarkhadzhiev
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Grand and Small Lebesgue Spaces and Their Analogs
Zeitschrift für Analysis und ihre Anwendungen, 2004We give the following, equivalent, explicit expressions for the norms of the small and grand Lebesgue spaces, which depend only on the non-decreasing rearrangement (we assume here that the underlying measure space has measure 1): \begin{align*} \|f\|_{L^{(p}} &\approx \int_0^1 (1-\ln t)^{
FIORENZA, ALBERTO, G. E. KARADZHOV
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Unilateral Ball Potentials in Grand Lebesgue Spaces
2021Necessary and sufficient conditions for the boundedness of unilateral ball potentials (ball fractional integrals) in grand Lebesgue spaces on \( \mathbb {R}^{n} \) were obtained for various classes of grandizers. Lower bounds are proved for the norm of these operators in grand spaces with integrable grandizers and upper bounds in spaces with radial ...
S. M. Umarkhadzhiev, M. U. Yakhshiboev
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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 +2 more
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Sawyer's duality principle for grand Lebesgue spaces
Mathematische Nachrichten, 2018AbstractThe 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 +3 more
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Recent Trends in Grand Lebesgue Spaces
2017The 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 +2 more
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Approximation in weighted generalized grand Lebesgue spaces
Colloquium Mathematicum, 2015Summary: 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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