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Generalized Grand Lebesgue Spaces Associated to Banach Function spaces [PDF]
Sahand Communications in Mathematical AnalysisIn this paper we introduce the class of grand Lebesgue spaces associated to a Banach function space $X$ by replacing the role of the $L^1$-norm by the norm $\|\cdot\|_X$ in the classical construction of the generalized grand Lebesgue spaces.
Alireza Bagheri Salec +2 more
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Identification of Fully Measurable Grand Lebesgue Spaces [PDF]
Journal of Function Spaces, 2017 We consider the Banach function spaces, called fully measurable grand Lebesgue spaces, associated with the function norm ρ(f)=ess supx∈Xδ(x)ρp(x)(f), where ρp(x) denotes the norm of the Lebesgue space of exponent p(x), and p(·) and δ(·) are measurable ...
Giuseppina Anatriello +2 more
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Approximation by matrix transform in generalized grand Lebesgue spaces with variable exponent
Journal of Numerical Analysis and Approximation Theory, 2021 In this work the Lipschitz subclass of the generalized grand Lebesgue space with variable exponent is defined and the error of approximation by matrix transforms in this subclass is estimated.
Ahmet Testici, Daniyal Israfilov
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Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this paper an elliptic operator of the $m$-th order $L$ with continuous coefficients in the $n$-dimensional domain $\Omega \subset R^{n} $ in the non-standard Grand-Sobolev space $W_{q)}^{m} \left(\Omega \right)\, $ generated by the norm $\left\| \,
Bilal Bilalov, Sabina Sadigova
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Molecular Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications
Mathematics, 2021 Let p→∈(0,∞)n be an exponent vector and A be a general expansive matrix on Rn. Let HAp→(Rn) be the anisotropic mixed-norm Hardy spaces associated with A defined via the non-tangential grand maximal function.
Jun Liu, Long Huang, Chenlong Yue
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Besov's Type Embedding Theorem for Bilateral Grand Lebesgue Spaces [PDF]
, 2010 In this paper we obtain the non-asymptotic norm estimations of Besov's type between the norms of a functions in different Bilateral Grand Lebesgue spaces (BGLS).
Ostrovsky, E., Sirota, L.
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Fractional integrals and derivatives: mapping properties [PDF]
, 2016 This survey is aimed at the audience of readers interested in the information on mapping properties of various forms of fractional integration operators, including multidimensional ones, in a large scale of various known function spaces.As is well known,
Rafeiro, Humberto, Samko, Stefan
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The Distance to L∞ in the Grand Orlicz Spaces
Journal of Function Spaces and Applications, 2013 We establish a formula for the distance to L∞ from the grand Orlicz space LΦ)Ω introduced in Capone et al. (2008). A new formula for the distance to L∞ from the grand Lebesgue space Ln)Ω introduced in Iwaniec and Sbordone (1992) is also provided.
Fernando Farroni, Raffaella Giova
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A Decomposition of the Dual Space of Some Banach Function Spaces
Journal of Function Spaces and Applications, 2012 We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space EXP𝛼 of the exponential integrable functions, the Marcinkiewicz space 𝐿𝑝,∞, and the Grand Lebesgue Space 𝐿𝑝),𝜃.
Claudia Capone, Maria Rosaria Formica
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Characterization of interpolation between Grand, small or classical Lebesgue spaces
, 2017 In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally $G\Gamma$-spaces. As a direct consequence of our results any Lorentz-Zygmund space $L^{a,r}({\rm Log}\,
Fiorenza, Aberto +4 more
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