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On the maximal function for rotation invariant measures in $ℝ^{n}$

Ana Vargas — 1994

Studia Mathematica

Given a positive measure μ in $ℝ^{n}$ , there is a natural variant of the noncentered Hardy-Littlewood maximal operator $M_{μ} f (x) = s u p_{x \in B} 1 / μ (B) ʃ_{B} | f | d μ$ , where the supremum is taken over all balls containing the point x. In this paper we restrict our attention to rotation invariant, strictly positive measures μ in $ℝ^{n}$ . We give some necessary and sufficient conditions for $M_{μ}$ to be bounded from $L^{1} (d μ)$ to $L^{1, \infty} (d μ)$ .

A smoothing property for the $L^{2}$ -critical NLS equations and an application to blowup theory

Sahbi Keraani; Ana Vargas — 2009

Annales de l'I.H.P. Analyse non linéaire

Checkerboards, Lipschitz functions and uniform rectifiability.

Peter W. Jones; Nets Hawk Katz; Ana Vargas — 1997

Revista Matemática Iberoamericana

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, H^n-1(∂Ω) = M < ∞ (depending on n and M) and a Lipschitz graph Γ (with constant L) such that H^n-1(Γ ∩ ∂Ω) ≥ ε. Here H^k...

A comparative analysis of recent identification approaches for discrete-event systems.

Estrada-Vargas, Ana Paula; López-Mellado, Ernesto; Lesage, Jean-Jacques — 2010

Mathematical Problems in Engineering

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Currently displaying 1 – 4 of 4

On the maximal function for rotation invariant measures in ℝ n

A smoothing property for the L 2 -critical NLS equations and an application to blowup theory

Checkerboards, Lipschitz functions and uniform rectifiability.

A comparative analysis of recent identification approaches for discrete-event systems.

On the maximal function for rotation invariant measures in $ℝ^{n}$

A smoothing property for the $L^{2}$ -critical NLS equations and an application to blowup theory