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Currently displaying 1 – 3 of 3

Order by Relevance | Title | Year of publication

Quasiconformal mappings preserving interpolating sequences.

González, María J.; Nicolau, Artur — 1998

Annales Academiae Scientiarum Fennicae. Mathematica

Symmetric and Zygmund measures in several variables

Evgueni Doubtsov; Artur Nicolau — 2002

Annales de l’institut Fourier

Let $ω : (0, \infty) \to (0, \infty)$ be a gauge function satisfying certain mid regularity conditions. A (signed) finite Borel measure $μ \in ℝ^{n}$ is called $ω$ -Zygmund if there exists a positive constant $C$ such that $| μ (Q_{+}) - μ (Q_{-}) | \leq C ω (ℓ (Q_{+})) | Q_{+} |$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size. Similarly, $μ$ is called an $ω$ - symmetric measure if there exists a positive constant $C$ such that $| μ (Q_{+}) / μ (Q_{-}) - 1 | \leq C ω (ℓ (Q_{+}))$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size, $ℓ (Q_{+}) = ℓ (Q_{-}) < 1$ . We characterize Zygmund and symmetric measures in terms of their harmonic extensions. Also, we show that the quadratic condition...

Multiplicative square functions.

María José González; Artur Nicolau — 2004

Revista Matemática Iberoamericana

We study regularity properties of a positive measure in the euclidean space in terms of two square functions which are the multiplicative analogues of the usual martingale square function and of the Lusin area function of a harmonic function. The size of ...

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