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Manor Mendel, Assaf Naor (2013)
Journal of the European Mathematical Society
It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type if and only if it is Markov -convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property.
P. Hajlasz, P. Koskela, H. Tuominen (2008)
Revista Matemática Iberoamericana
Mikhail I. Ostrovskii (2014)
Fundamenta Mathematicae
We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikodým property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that no thick family of geodesics is Markov convex, and comparing this result with results of Cheeger-Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon-Nikodým property contains a bilipschitz...
Loukas Grafakos, Liguang Liu, Diego Maldonado, Dachun Yang (2014)
The Anh Bui, Jun Cao, Luong Dang Ky, Dachun Yang, Sibei Yang (2013)
Analysis and Geometry in Metric Spaces
Let X be a metric space with doubling measure and L a one-to-one operator of type ω having a bounded H∞ -functional calculus in L2(X) satisfying the reinforced (pL; qL) off-diagonal estimates on balls, where pL ∊ [1; 2) and qL ∊ (2;∞]. Let φ : X × [0;∞) → [0;∞) be a function such that φ (x;·) is an Orlicz function, φ(·;t) ∊ A∞(X) (the class of uniformly Muckenhoupt weights), its uniformly critical upper type index l(φ) ∊ (0;1] and φ(·; t) satisfies the uniformly reverse Hölder inequality of order...
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