On the properties of quasi-Banach function spaces

DOI10.1007/S12220-024-01673-YMaRDI QIDQ6544543

Aleš Nekvinda, Dalimil Peša

Publication date: 27 May 2024

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

separabilityquasi-Banach spacequasinormdilation operatorquasi-Banach function spacegeneralised Riesz-Fischer theorem

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) Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16)

Cites Work

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• Linear operators, Fourier integral operators and \(k\)-plane transforms on rearrangement-invariant quasi-Banach function spaces
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• Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
• Real-variable theory of Hardy spaces associated with generalized Herz spaces of Rafeiro and Samko
• Weak Hardy spaces associated with ball quasi-Banach function spaces on spaces of homogeneous type: decompositions, real interpolation, and Calderón-Zygmund operators
• Hardy spaces associated with ball quasi-Banach function spaces on spaces of homogeneous type: Littlewood-Paley characterizations with applications to boundedness of Calderón-Zygmund operators
• Sobolev embeddings, rearrangement-invariant spaces and Frostman measures
• Sublinear operators on radial rearrangement-invariant quasi-Banach function spaces
• Applications of Hardy spaces associated with ball quasi-Banach function spaces
• Sobolev embeddings in Orlicz and Lorentz spaces with measures
• Fractional integral operators on Morrey spaces built on rearrangement-invariant quasi-Banach function spaces
• Compactness characterizations of commutators on ball Banach function spaces
• Newtonian spaces based on quasi-Banach function lattices
• Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices
• Normability of Lorentz spaces—an alternative approach
• Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces
• FOURIER-TYPE TRANSFORMS ON REARRANGEMENT-INVARIANT QUASI-BANACH FUNCTION SPACES
• On relatively compact sets in quasi-Banach function spaces
• Optimal estimates for the fractional Hardy operator
• Hardy spaces for ball quasi-Banach function spaces
• Fourier integrals and Sobolev embedding on rearrangement invariant quasi-Banach function spaces
• Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces
• Riesz transform characterization of Hardy spaces associated with ball quasi-Banach function spaces
• Basic functional properties of certain scale of rearrangement‐invariant spaces
• Extrapolation in general quasi-Banach function spaces
• Fractional Leibniz rules in the setting of quasi-Banach function spaces
• Gagliardo representation of norms of ball quasi-Banach function spaces

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