Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition in variable exponent Sobolev spaces

DOI10.1007/s10114-015-4488-xzbMath1339.46033OpenAlexW978787100MaRDI QIDQ2354167

Guozhen Lu, Xia Li, Hanli Tang

Publication date: 10 July 2015

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-015-4488-x

zbMATH Keywords

representation formulastratified Lie groupsfractional integrals on homogeneous spacesnon-isotropic Sobolev spaces with variable exponentsPoincaré inequalities with variable exponentsSobolev inequalities with variable exponentsvector fields satisfying Hörmander's condition

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (7)

A \({\mathtt p}(\cdot )\)-Poincaré-type inequality for variable exponent Sobolev spaces with zero boundary values in Carnot groups ⋮ Multilinear singular integral operators with generalized kernels and their multilinear commutators ⋮ Interior \(W^{2, p(x)}\)-regularity for elliptic equations of nondivergence form ⋮ Coercive inequalities and U-bounds on step-two Carnot groups ⋮ \(q\)-Poincaré inequalities on Carnot groups with filiform type Lie algebra ⋮ Coercive inequalities in higher-dimensional anisotropic Heisenberg group ⋮ Correction to: ``A \({\mathtt{p}}({\cdot })\)-Poincaré-type inequality for variable exponent Sobolev spaces with zero boundary values in Carnot groups

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