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( H p , L p ) -type inequalities for the two-dimensional dyadic derivative

Ferenc Weisz (1996)

Studia Mathematica

It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space H p , q to L p , q (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type ( L 1 , L 1 ) . As a consequence we show that the dyadic integral of a ∞ function f ∈ L 1 is dyadically differentiable and its derivative is f a.e.

A spectral gap theorem in SU ( d )

Jean Bourgain, Alex Gamburd (2012)

Journal of the European Mathematical Society

We establish the spectral gap property for dense subgroups of SU ( d ) ( d ≥ 2 ) , generated by finitely many elements with algebraic entries; this result was announced...

Amenable hyperbolic groups

Pierre-Emmanuel Caprace, Yves de Cornulier, Nicolas Monod, Romain Tessera (2015)

Journal of the European Mathematical Society

We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...

Haar system on a product of zero-dimensional compact groups

Sergei Lukomskii (2011)

Open Mathematics

In this work, we study the problem of constructing Haar bases on a product of arbitrary compact zero-dimensional Abelian groups. A general scheme for the construction of Haar functions is given for arbitrary dimension. For dimension d=2, we describe all Haar functions.

Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients

Péter Simon, Ferenc Weisz (1997)

Studia Mathematica

Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) ( ∑ k = 1 ∞ ∑ j = 1 ∞ | f ̂ ( k , j ) | p ( k j ) p - 2 ) 1 / p ≤ C p ∥ f ∥ H * * p (1/2 < p≤2) where f belongs to the Hardy space H * * p ( G m × G s ) defined by means of a maximal function. This inequality is extended to p > 2 if the Vilenkin-Fourier coefficients of f form a monotone sequence. We show that the converse of (*) also holds for all p > 0 under the monotonicity assumption.

Large scale behavior of semiflexible heteropolymers

Francesco Caravenna, Giambattista Giacomin, Massimiliano Gubinelli (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the disorder) are modeled in terms of random rotations. We focus on the quenched regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative...

Multiplicative Systems on Ultra-Metric Spaces

Memic, Nacima (2010)

Mathematica Balkanica New Series

AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75We perform analysis of certain aspects of approximation in multiplicative systems that appear as duals of ultrametric structures, e.g. in cases of local fields, totally disconnected Abelian groups satisfying the second axiom of countability or more general ultrametric spaces that do not necessarily possess a group structure. Using the fact that the unit sphere of a local field is a Vilenkin group, we introduce a new concept of differentiation in...

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