Higher‐order Sobolev‐type embeddings on Carnot–Carathéodory spaces

DOI10.1002/mana.201500418zbMath1377.46019OpenAlexW2514236009MaRDI QIDQ5272515

Martin Franců

Publication date: 29 June 2017

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

Full work available at URL: https://doi.org/10.1002/mana.201500418

zbMATH Keywords

rearrangement-invariant spacesCarnot-Carathéodory spaceshigher-order Sobolev embeddings

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) Sub-Riemannian geometry (53C17)

Related Items

Higher-order compact embeddings of function spaces on Carnot-Carathéodory spaces, Rearrangements in Carnot groups

Cites Work

• Improved Gagliardo-Nirenberg inequalities on Heisenberg type groups
• The Moser-Trudinger inequality in unbounded domains of Heisenberg group and sub-elliptic equations
• Improved Sobolev inequalities and Muckenhoupt weights on stratified Lie groups
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Sub-elliptic global high order Poincaré inequalities in stratified Lie groups and applications
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Kelvin transforms and harmonic polynomials on the Heisenberg group
• Balls and metrics defined by vector fields. I: Basic properties
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• The Brunn-Minkowski inequality in Gauss space
• Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for Carnot-Carathéodory metrics
• Sobolev embeddings into BMO, VMO, and \(L_{\infty}\)
• Best constants for Moser-Trudinger inequalities, fundamental solutions and one-parameter representation formulas on groups of Heisenberg type
• On critical cases of Sobolev's inequalities for Heisenberg groups
• Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
• Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups
• Higher-order multilinear Poincaré and Sobolev inequalities in Carnot groups
• Higher-order Sobolev embeddings and isoperimetric inequalities
• Isoperimetry between exponential and Gaussian
• Hypoelliptic second order differential equations
• Normal and integral currents
• Extremals for the Sobolev Inequality on the Heisenberg Group and the CR Yamabe Problem
• Best constants for Moser-Trudinger inequalities on the Heisenberg group
• Regular domains in homogeneous groups
• Trudinger‐Moser inequalities on the entire Heisenberg group
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]
• Orlicz-Sobolev boundary trace embeddings