Real interpolation of small Lebesgue spaces in a critical case

DOI10.1155/2018/3298582zbMath1405.46016OpenAlexW2885613128WikidataQ129406729 ScholiaQ129406729MaRDI QIDQ1671179

Irshaad Ahmed, Ghulam Murtaza, Aneesa Hafeez

Publication date: 6 September 2018

Published in: Journal of Function Spaces (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/3298582

zbMATH Keywords

interpolationsmall 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) Interpolation between normed linear spaces (46B70)

Related Items (6)

On Hardy type inequalities in grand Lebesgue spacesL_p)for 0 <p≤ 1 ⋮ Interpolation of generalized gamma spaces in a critical case ⋮ General reiteration theorems for \(\mathcal{R}\) and \(\mathcal{L}\) classes: case of right \(\mathcal{R}\)-spaces and left \(\mathcal{L}\)-spaces ⋮ Reiteration formulae for the real interpolation method including \(\mathcal{L}\) or \(\mathcal{R}\) limiting spaces ⋮ General reiteration theorems for \(\mathcal{R}\) and \(\mathcal{L}\) classes: case of left \(\mathcal{R} \)-spaces and right \(\mathcal{L} \)-spaces ⋮ Some new results related to Lorentz \(G\Gamma\)-spaces and interpolation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compactness, interpolation inequalities for small Lebesgue-Sobolev spaces and applications
• A direct approach to the duality of grand and small Lebesgue spaces
• New properties of small Lebesgue spaces and their applications
• Some new applications of the pointwise relations for the relative rearrangement
• Duality and reflexivity in grand Lebesgue spaces
• Characterization of interpolation between grand, small or classical Lebesgue spaces
• Sharp embeddings of Besov spaces with logarithmic smoothness in sub-critical cases
• Grand and small Lebesgue spaces and their analogs
• An improvement of dimension-free Sobolev imbeddings in r.i. spaces
• General Holmstedt's formulae for the \(K\)-functional
• Some estimates in \(G\Gamma (p,m,w)\) spaces
• Tractable embeddings of Besov spaces into small Lebesgue spaces
• Reiteration theorems for the K -interpolation method in limiting cases
• On grand and small Lebesgue and Sobolev spaces and some applications to PDE's
• Relative rearrangement method for estimating dual norms

This page was built for publication: Real interpolation of small Lebesgue spaces in a critical case