Oscillation of Generalized Differences of Hölder and Zygmund Functions

Alejandro J. Castro; José G. Llorente; Artur Nicolau

doi:10.1007/s12220-017-9882-4

Oscillation of Generalized Differences of Hölder and Zygmund Functions

Alejandro J. Castro, José G. Llorente, Artur Nicolau

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper we analyze the oscillation of functions having derivatives in the Hölder or Zygmund class in terms of generalized differences and prove that its growth is governed by a version of the classical Kolmogorov’s Law of the Iterated Logarithm. A better behavior is obtained for functions in the Lipschitz class via an interesting connection with Calderón–Zygmund operators.

Original language	English
Pages (from-to)	1-22
Number of pages	22
Journal	Journal of Geometric Analysis
DOIs	https://doi.org/10.1007/s12220-017-9882-4
Publication status	Accepted/In press - Jun 20 2017

Keywords

Calderón–Zygmund operators
Generalized differences
Hölder functions
Law of the iterated logarithm
Lipschitz functions
Martingales
Oscillation
Zygmund class

ASJC Scopus subject areas

Geometry and Topology

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abstract = "In this paper we analyze the oscillation of functions having derivatives in the H{\"o}lder or Zygmund class in terms of generalized differences and prove that its growth is governed by a version of the classical Kolmogorov{\textquoteright}s Law of the Iterated Logarithm. A better behavior is obtained for functions in the Lipschitz class via an interesting connection with Calder{\'o}n–Zygmund operators.",

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AU - Llorente, José G.

AU - Nicolau, Artur

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KW - Hölder functions

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KW - Lipschitz functions

KW - Martingales

KW - Oscillation

KW - Zygmund class

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