Displaying similar documents to “Decreasing rearrangements and L p , q of the Bohr group”

Checkerboards, Lipschitz functions and uniform rectifiability.

Peter W. Jones, Nets Hawk Katz, Ana Vargas (1997)

Revista Matemática Iberoamericana

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In his recent lecture at the International Congress [S], Stephen Semmes stated the following conjecture for which we provide a proof. Theorem. Suppose Ω is a bounded open set in Rn with n > 2, and suppose that B(0,1) ⊂ Ω, Hn-1(∂Ω) = M < ∞ (depending on n and M) and a Lipschitz graph Γ (with constant L) such that Hn-1(Γ ∩ ∂Ω) ≥ ε. Here H...

Quadratic tilt-excess decay and strong maximum principle for varifolds

Reiner Schätzle (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper, we prove that integral n -varifolds μ in codimension 1 with H μ ∈ L loc p ( μ ) , p > n , p ≥ 2 have quadratic tilt-excess decay tiltex μ ( x , ϱ , T x μ ) = O x ( ϱ 2 ) for μ -almost all x , and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature H μ , unless the smooth manifold is locally contained in the support of μ .

Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces

Luigi Ambrosio, Alessio Figalli (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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We study points of density 1 / 2 of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this class of points. Here density 1 / 2 is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.