We consider quasisymmetric reparametrizations of the parameter space of the quadratic family. We prove that the set of quadratic maps which are either regular or Collet-Eckmann with polynomial recurrence of the critical orbit has full Lebesgue measure.

In this note we shall give examples of rational maps on the Riemann sphere and also of polynomial interval maps which are transitive but not ergodic with respect to Lebesgue measure. In fact, these maps have two disjoint compact attrac-tors whose attractive basins arèintermingled', each having a positive Lebesgue measure in every open set. In addition, we show that there exists a real bi-modal ...

Abstract The purpose of this paper is to quantify the size Lebesgue constants $(\boldsymbol {L}_m)_{m=1}^{\infty }$ associated with thresholding greedy algorithm in terms a new generation parameters that modulate accurately some features general basis. This fine tuning allows us provide an answer question raised by Temlyakov 2011 find natural sequence greedy-type for arbitrary bases Banach (or ...

Let G be a bounded open subset of Euclidean space with real algebraic boundary Γ. Under the assumption that the degree d of Γ is given, and the power moments of the Lebesgue measure on G are known up to order 3d, we describe an algorithmic procedure for obtaining a polynomial vanishing on Γ. The particular case of semialgebraic sets defined by a single polynomial inequality raises an intriguing...

Let G be a bounded open subset of Euclidean space with real algebraic boundary Γ. Under the assumption that the degree d of Γ is given, and the power moments of the Lebesgue measure on G are known up to order 3d, we describe an algorithmic procedure for obtaining a polynomial vanishing on Γ. The particular case of semialgebraic sets defined by a single polynomial inequality raises an intriguing...

We consider a multidimensional Burgers equation on the torus T and the whole space R . We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we also provide estimates on the large time behaviour of solutions. In the case of R we establish the existence of a unique global solution if a Beale-Kato-Majda type condition is satisfied. To prove thes...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...

We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly.

Abstract. Let (X, d, μ) be a metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions, which is called nonhomogeneous metric measure space. In this paper, via a sharp maximal operator, the boundedness of commutators generated by multilinear singular integral with RBMO(μ) function on non-homogeneous metric measure spaces in m-multiple Lebesgue spa...