Results 1 to 10 of about 56,362 (113)
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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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.
Cruz-Uribe, D. +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 $G $-spaces. As a direct consequence of our results any Lorentz-Zygmund space $L^{a,r}({\rm Log}\, L)^ $, is an interpolation space in the sense of Peetre between either two Grand Lebesgue spaces or ...
Fiorenza, Alberto +4 more
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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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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):
Giovanni Di Fratta, Alberto 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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Bilinear multipliers of small Lebesgue spaces
TURKISH JOURNAL OF MATHEMATICS, 2021 Let $G$ be a locally compact abelian metric group with Haar measure $\lambda $ and $\hat{G}$ its dual with Haar measure $\mu ,$ and $\lambda ( 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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Gradient estimates in generalized Orlicz spaces for quasilinear elliptic equations via extrapolation
AIMS Mathematics, 2023 The gradient estimates in the generalized Orlicz space for weak solutions of a class of quasi-linear elliptic boundary value problems are obtained using the modern technique of extrapolation.
Ruimin Wu , Yinsheng Jiang, Liyuan Wang
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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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