Grand Lebesgue space for p = ∞ and its application to Sobolev–Adams embedding theorems in borderline cases

DOI10.1002/mana.202000347OpenAlexW4220779977MaRDI QIDQ6093918

Humberto Rafeiro, Stefan G. Samko, Salaudin Umarkhadzhiev

Publication date: 9 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.202000347

zbMATH Keywords

BMORiesz potential operatorgrand Lebesgue spaces

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Fractional derivatives and integrals (26A33)

Related Items (6)

Local grand Lebesgue spaces on quasi-metric measure spaces and some applications ⋮ Local grand variable exponent Lebesgue spaces ⋮ Grand and small norms in Lebesgue spaces ⋮ A new approach to grand and small norms in discrete Lebesgue spaces ⋮ Professor Stefan G. Samko research: a decade retrospective ⋮ Fractional operators from vanishing Morrey to vanishing Campanato spaces in the variable exponent setting on quasi-metric measure spaces

Cites Work

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• Weighted Hardy operators in the local generalized vanishing Morrey spaces
• Maximal, potential and singular operators in vanishing generalized Morrey spaces
• Generalization of the notion of grand Lebesgue space
• Integral operators in non-standard function spaces. Volume 1: Variable exponent Lebesgue and amalgam spaces
• Integral operators in non-standard function spaces. Volume 2: Variable exponent Hölder, Morrey-Campanato and Grand spaces
• Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces
• On the integrability of the Jacobian under minimal hypotheses
• Inverting the \(p\)-harmonic operator
• Grand Lebesgue sequence spaces
• Herz spaces meet Morrey type spaces and complementary Morrey type spaces
• BMO-VMO results for fractional integrals in variable exponent Morrey spaces
• A note on Riesz fractional integrals in the limiting case \(\alpha(x)p(x) \equiv n\)
• Necessary and sufficient conditions for the boundedness of fractional maximal operators in local Morrey-type spaces
• Boundedness of translation invariant operators on Hölder spaces and \(L^ p\)-spaces
• On the theory of \({\mathcal L}_{p, \lambda}\) spaces
• Riesz fractional integrals in grand Lebesgue spaces on \(\mathbb{R}^{n}\)
• Boundedness of commutators of singular and potential operators in generalized grand Morrey spaces and some applications
• An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
• Maximal functions, potentials and singular integrals in grand Morrey spaces
• Гранд-пространства типа Морри
• Sobolev imbedding theorems in borderline cases
• A Note on Boundedness of Operators in Grand Grand Morrey Spaces
• Riesz type potential operators in generalized grand Morrey spaces
• The Boundedness of the Riesz Potential Operator from Generalized Grand Lebesgue Spaces to Generalized Grand Morrey Spaces
• Estimates for nondivergence elliptic equations with VMO coefficients in generalized grand Morrey spaces
• Criteria for the Boundedness of Potential Operators in Grand Lebesgue Spaces

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