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

Department of Mathematics

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

1 Citation (Scopus)

Abstract

© 2017, Mathematica Josephina, Inc. 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)	1665-1686
Journal	Journal of Geometric Analysis
Volume	28
Issue number	2
DOIs	https://doi.org/10.1007/s12220-017-9882-4
Publication status	Published - 1 Apr 2018

Keywords

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

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title = "Oscillation of Generalized Differences of H{\"o}lder and Zygmund Functions",

abstract = "{\textcopyright} 2017, Mathematica Josephina, Inc. 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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author = "Castro, {Alejandro J.} and Llorente, {Jos{\'e} G.} and Artur Nicolau",

year = "2018",

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T1 - Oscillation of Generalized Differences of Hölder and Zygmund Functions

AU - Castro, Alejandro J.

AU - Llorente, José G.

AU - Nicolau, Artur

PY - 2018/4/1

Y1 - 2018/4/1

N2 - © 2017, Mathematica Josephina, Inc. 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.

AB - © 2017, Mathematica Josephina, Inc. 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.

KW - Calderón–Zygmund operators

KW - Generalized differences

KW - Hölder functions

KW - Law of the iterated logarithm

KW - Lipschitz functions

KW - Martingales

KW - Oscillation

KW - Zygmund class

U2 - 10.1007/s12220-017-9882-4

DO - 10.1007/s12220-017-9882-4

M3 - Article

VL - 28

SP - 1665

EP - 1686

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

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