On estimates for the Besov norms of solutions to 3D subelliptic equations

DOI10.1134/S003744661105017XzbMath1242.35106OpenAlexW2117688600MaRDI QIDQ665906

N. N. Romanovskiĭ

Publication date: 7 March 2012

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s003744661105017x

zbMATH Keywords

singular integral operatorHeisenberg groupembedding theoremBesov spacesSchauder estimates

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Cites Work

• Fundamental solutions and geometry of the sum of squares of vector fields
• Intégrales de Fourier quadratiques et calcul symbolique exact sur le groupe d'Heisenberg. (Quadratic Fourier integrals and exact symbolic calculus on the Heisenberg group)
• Asymptotics for some Green kernels on the Heisenberg group and the Martin boundary
• \(L^p\)-estimates for the wave equation on the Heisenberg group
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Extension of differentiable functions beyond the boundary of the domain on Carnot groups
• Trace theorems for vector fields
• Sobolev and Morrey estimates for non-smooth vector fields of step two
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces
• Hypoelliptic second order differential equations
• Intertwining operators for semisimple groups
• Regularity for quasilinear second‐order subelliptic equations
• Pointwise Schauder estimates for second order linear equations in Carnot groups
• Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces
• A fundamental solution for a subelliptic operator
• A Whitney extension theorem in \(L^p\) and Besov spaces
• Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces
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