Continuous and Compact Embeddings of Bessel-Potential-Type Spaces

DOI10.1007/978-3-0348-0263-5_10zbMath1261.26002OpenAlexW244233509MaRDI QIDQ2914471

Bohumír Opic

Publication date: 20 September 2012

Published in: Spectral Theory, Function Spaces and Inequalities (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0263-5_10

zbMATH Keywords

compact embeddingsslowly varying functionscontinuous embeddingsrearrangement-invariant Banach function spacesBessel potentialsHölder-type spaces(fractional) Sobolev-type spacesLorentz-Karamata 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) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Lipschitz (Hölder) classes (26A16) Linear operators on function spaces (general) (47B38) Inequalities for sums, series and integrals (26D15) Rate of growth of functions, orders of infinity, slowly varying functions (26A12) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (2)

Quantitative estimates of embedding constants for Gagliardo-Nirenberg inequalities on critical Sobolev-Besov-Lorentz spaces ⋮ Iterated grand and small Lebesgue spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal embeddings of generalized Bessel and Riesz potentials
• Compact embeddings of Bessel-potential-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness
• Theory of Bessel potentials. I
• Weak type inequalities for moduli of smoothness: The case of limit value parameters
• Optimal embeddings and compact embeddings of Bessel-potential-type spaces
• Weak interpolation in Banach spaces
• Extrapolation and optimal decompositions: with applications to analysis
• On embeddings of logarithmic Bessel potential spaces
• Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
• Regular variation and differential equations
• Optimal embeddings of Bessel-potential-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness
• Non-compact and sharp embeddings of logarithmic Bessel potential spaces into Hölder-type spaces
• Optimality of embeddings of Bessel-potential-type spaces into generalized Hölder spaces
• On spaces of potentials connected with \(L^ p\) classes
• On the theory of spaces \(\Lambda\)
• On embeddings between classical Lorentz spaces
• Compactness properties of Sobolev imbeddings for rearrangement invariant norms
• On compactness of Sobolev embeddings in rearrangement-invariant spaces
• Sharp estimates of the k -modulus of smoothness of Bessel potentials
• Sharpness and non‐compactness of embeddings of Bessel‐potential‐type spaces
• Optimality of Function Spaces in Sobolev Embeddings
• Shorter Notes: On the Differentiability of Functions in R n
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Weakly Differentiable Functions
• On generalized Lorentz-Zygmund spaces
• Spaces of Bessel‐potential type and embeddings: the super‐limiting case
• Optimality of embeddings of logarithmic Bessel potential spaces
• Real Interpolation with Logarithmic Functors and Reiteration
• Limiting reiteration for real interpolation with slowly varying functions
• Optimality of embeddings of Bessel-potential-type spaces into Lorentz–Karamata spaces
• Compact and continuous embeddings of logarithmic Bessel potential spaces
• Sharpness of embeddings in logarithmic Bessel-potential spaces
• Interpolation of Operators on Scales of Generalized Lorentz-Zygmund Spaces
• Lorentz–Karamata spaces, Bessel and Riesz potentials and embeddings
• Logarithmic Sobolev Spaces and Their Applications to Spectral Theory
• Compactness of Sobolev imbeddings involving rearrangement-invariant norms

This page was built for publication: Continuous and Compact Embeddings of Bessel-Potential-Type Spaces