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The multifractal box dimensions of typical measures

Frédéric Bayart (2012)

Fundamenta Mathematicae

We compute the typical (in the sense of Baire’s category theorem) multifractal box dimensions of measures on a compact subset of d . Our results are new even in the context of box dimensions of measures.

The one-sided ergodic Hilbert transform in Banach spaces

Guy Cohen, Christophe Cuny, Michael Lin (2010)

Studia Mathematica

Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform l i m n k = 1 n ( T k x ) / k . We prove that weak and strong convergence are equivalent, and in a reflexive space also s u p n | | k = 1 n ( T k x ) / k | | < is equivalent to the convergence. We also show that - k = 1 ( T k ) / k (which converges on (I-T)X) is precisely the infinitesimal generator of the semigroup ( I - T ) | ( I - T ) X ¯ r .

The Peano curves as limit of α-dense curves.

G. Mora (2005)

RACSAM

En este artículo presentamos una caracterización de las curvas de Peano como límite uniforme de sucesiones de curvas α-densas en el compacto que es llenado por la curva de Peano. Estas curvas α-densas deben tener densidades tendiendo a cero y sus funciones coordenadas deben de ser de variación tendiendo a infinito cuando α tiende a cero.

The Poincaré Inequality Does Not Improve with Blow-Up

Andrea Schioppa (2016)

Analysis and Geometry in Metric Spaces

For each β > 1 we construct a family Fβ of metric measure spaces which is closed under the operation of taking weak-tangents (i.e. blow-ups), and such that each element of Fβ admits a (1, P)-Poincaré inequality if and only if P > β.

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