Some Hardy and Rellich type inequalities for affine connections

Some Hardy and Rellich type inequalities for affine connections

In this article we study various forms of the Hardy inequality for affine connections on a complete noncompact Riemannian manifold, including the two-weight Hardy inequality, the improved Hardy inequality, the Rellich inequality, the Hardy–Poincaré inequality and the Heisenberg–Pauli–Weyl inequality...

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Veröffentlicht in:Journal of pseudo-differential operators and applications 2024-09, Vol.15 (3), Article 67
Hauptverfasser: Wang, Pengyan, Chang, Huiting
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Functional Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Partial Differential Equations
Riemann manifold
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Zusammenfassung:In this article we study various forms of the Hardy inequality for affine connections on a complete noncompact Riemannian manifold, including the two-weight Hardy inequality, the improved Hardy inequality, the Rellich inequality, the Hardy–Poincaré inequality and the Heisenberg–Pauli–Weyl inequality. Our results improve and include many previously known results as special cases.
ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-024-00639-6