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Representation formulas and weighted Poincaré inequalities for Hörmander vector fields

Bruno Franchi, Guozhen Lu, Richard L. Wheeden (1995)

Annales de l'institut Fourier

We derive weighted Poincaré inequalities for vector fields which satisfy the Hörmander condition, including new results in the unweighted case. We also derive a new integral representation formula for a function in terms of the vector fields applied to the function. As a corollary of the L 1 versions of Poincaré’s inequality, we obtain relative isoperimetric inequalities.

Representation of bilinear forms in non-Archimedean Hilbert space by linear operators

Toka Diagana (2006)

Commentationes Mathematicae Universitatis Carolinae

The paper considers representing symmetric, non-degenerate, bilinear forms on some non-Archimedean Hilbert spaces by linear operators. Namely, upon making some assumptions it will be shown that if φ is a symmetric, non-degenerate bilinear form on a non-Archimedean Hilbert space, then φ is representable by a unique self-adjoint (possibly unbounded) operator A .

Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II

Dodzi Attimu, Toka Diagana (2007)

Commentationes Mathematicae Universitatis Carolinae

The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space 𝔼 ω × 𝔼 ω by linear operators. More precisely, upon making some suitable assumptions we prove that if ϕ is a non-degenerate bilinear form on 𝔼 ω × 𝔼 ω , then ϕ is representable by a unique linear operator A whose adjoint operator A * exists.

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