Compactness properties of Sobolev imbeddings for rearrangement invariant norms

DOI10.1090/S0002-9947-06-04203-6zbMath1116.46023OpenAlexW1988703377MaRDI QIDQ3420364

Guillermo P. Curbera, Werner J. Ricker

Publication date: 1 February 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-06-04203-6

zbMATH Keywords

compactnessrearrangement invariant spacesSobolev imbeddingsoptimal domains

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)

Related Items (18)

Continuous and Compact Embeddings of Bessel-Potential-Type Spaces ⋮ Bounds on the joint and generalized spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators ⋮ Optimal Sobolev type inequalities in Lorentz spaces ⋮ Estimates for continuity envelopes and approximation numbers of Bessel potentials ⋮ Optimal extension of Fourier multiplier operators in \(L^p(G)\) ⋮ Function spaces arising from kernel operators ⋮ Inequalities and equalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators ⋮ Sobolev type inequalities for rearrangement invariant spaces ⋮ Logarithmic convexity of fixed points of stochastic kernel operators ⋮ Optimal extension of the Hausdorff-Young inequality ⋮ Optimal domains for \(L^{0}\)-valued operators via stochastic measures ⋮ Solid extensions of the Cesàro operator on the Hardy space \(H^2(\mathbb D)\) ⋮ Salem sets in local fields, the Fourier restriction phenomenon and the Hausdorff-Young inequality ⋮ Inequalities on the spectral radius, operator norm and numerical radius of the Hadamard weighted geometric mean of positive kernel operators ⋮ Inequalities for the spectral radius and essential spectral radius of positive operators on Banach sequence spaces ⋮ Inequalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators ⋮ Inversion and extension of the finite Hilbert transform on \((-1,1)\) ⋮ Hadamard weighted geometric mean inequalities for the spectral and essential spectral radius of positive operators on Banach function and sequence spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• When \(L^ 1\) of a vector measure is an AL-space
• Sobolev embeddings into BMO, VMO, and \(L_{\infty}\)
• Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
• Orlicz-Sobolev spaces and imbedding theorems
• On integrability and summability in vector spaces
• Weakly Differentiable Functions
• A sharp exponential inequality for Lorentz-Sobolev spaces on bounded domains
• Optimal domains for the kernel operator associated with Sobolev's inequality
• Interpolation of Operators on Scales of Generalized Lorentz-Zygmund Spaces
• Sobolev imbedding theorems in borderline cases
• Poincaré and Friedrichs inequalities in abstract Sobolev spaces

This page was built for publication: Compactness properties of Sobolev imbeddings for rearrangement invariant norms