Results 1 to 10 of about 659 (99)
On small Lebesgue spaces [PDF]
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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Real Interpolation of Small Lebesgue Spaces in a Critical Case
Journal of Function Spaces, 2018 We establish an interpolation formula for small Lebesgue spaces in a critical case.
Irshaad Ahmed +2 more
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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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Fully measurable small Lebesgue spaces
Journal of Mathematical Analysis and Applications, 2017 The interval \([0,1]\) of the real line \(\mathbb R=[-\infty,\infty]\) is denoted by \(I\), the class of Lebesgue measurable functions on \(I\) is denoted by \({\mathcal M}\) and the class of essentially bounded functions on \(I\) is denoted by \(L^\infty(I)\), so that \(L^\infty(I)= \{f\in{\mathcal M}(I):\| f\|_\infty a)= 0\}\). If \(p(.)\in\mathcal{M}
Raffaella Giova +2 more
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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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Bilinear multipliers of small Lebesgue spaces
TURKISH JOURNAL OF MATHEMATICS, 2021 Let $G$ be a locally compact abelian metric group with Haar measure $λ$ and $\hat{G}$ its dual with Haar measure $μ,$ and $λ( G) $ is finite.
Öznur KULAK, A.Turan GÜRKANLI
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Uniform estimates with data from generalized Lebesgue spaces in periodic structures
Boundary Value Problems, 2021 We study various types of uniform Calderón–Zygmund estimates for weak solutions to elliptic equations in periodic homogenization. A global regularity is obtained with respect to the nonhomogeneous term from weighted Lebesgue spaces, Orlicz spaces, and ...
Yunsoo Jang
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Karpatsʹkì Matematičnì Publìkacìï, 2021 Dirichlet-Neumann problem for the typeless high order partial differential equation with deviating over the space argument is studied in the domain, which is the Cartesian product of the segment $(0,T)$ and the unit circle $\Omega=\mathbb R/(2\pi \mathbb
P.Ya. Pukach +3 more
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Global gradient estimates for Dirichlet problems of elliptic operators with a BMO antisymmetric part
Advances in Nonlinear Analysis, 2022 Let n≥2n\ge 2 and Ω⊂Rn\Omega \subset {{\mathbb{R}}}^{n} be a bounded nontangentially accessible domain. In this article, the authors investigate (weighted) global gradient estimates for Dirichlet boundary value problems of second-order elliptic equations
Yang Sibei, Yang Dachun, Yuan Wen
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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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