Results 1 to 10 of about 47 (45)
Embeddings between grand, small, and variable Lebesgue spaces [PDF]
Mathematical Notes, 2017 We give conditions on the exponent function $p(\cdot)$ that imply the existence of embeddings between grand, small and variable Lebesgue spaces. We construct examples to show that our results are close to optimal. Our work extends recent results by the second author, Rakotoson and Sbordone.
A Fiorenza
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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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On grand and small Lebesgue and Sobolev spaces and some applications to PDE's [PDF]
Differential Equations & Applications, 2018 Summary: This paper is essentially a survey on grand and small Lebesgue spaces, which are rearrangement-invariant Banach function spaces of interest not only from the point of view of function spaces theory, but also from the point of view of their applications: the corresponding Sobolev spaces are of interest, for instance, in the theory of PDEs.
Fiorenza, Alberto +2 more
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Characterization of interpolation between Grand, small or classical Lebesgue spaces [PDF]
Nonlinear Analysis, 2018 In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally $GΓ$-spaces. As a direct consequence of our results any Lorentz-Zygmund space $L^{a,r}({\rm Log}\, L)^β$, is an interpolation space in the sense of Peetre between either two Grand Lebesgue spaces or ...
Fiorenza, Alberto +4 more
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A direct approach to the duality of grand and small Lebesgue spaces [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2009 Let \(\mathcal{M}_{0}\) be the set of all Lebesgue measurable function in the interval \((0,1)\), finite a.e.\ in it and let \(\mathcal{M}_{0}^{+}\) be the class of all nonnegative functions of \(\mathcal{M}_{0}\). For \(f \in \mathcal{M}_{0}\), the decreasing rearrangement \(f^{*}\) of \(f\) is defined by \[ f^{*} = \inf\{ \lambda > 0: |\{x \in (0,1):
G. DI FRATTA, FIORENZA, ALBERTO
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Journal of Function Spaces and Applications, 2005 We consider a generalized version of the small Lebesgue spaces, introduced in [5] as the associate spaces of the grand Lebesgue spaces. We find a simplified expression for the norm, prove relevant properties, compute the fundamental function and discuss ...
Claudia Capone, Alberto Fiorenza
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International Journal of Analysis and ApplicationsIn this article, we investigate limiting real interpolation spaces. Our primary goal is to thoroughly explore and establish the interpolation properties within critical cases θ = 0 and θ = 1 for Lorentz spaces, Grand and Small Lebesgue spaces as well as for Besov spaces modelled on so called Lorentz-Zygmund spaces.
Muhammad Awais +3 more
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A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks. [PDF]
Patterns (N Y), 2021 Uthamacumaran A.
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