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

Departament de Matemàtiques

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1 Citació (Scopus)

Resum

© 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.

Idioma original	Anglès
Pàgines (de-a)	1665-1686
Revista	Journal of Geometric Analysis
Volum	28
Número	2
DOIs	https://doi.org/10.1007/s12220-017-9882-4
Estat de la publicació	Publicada - 1 d’abr. 2018

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10.1007/s12220-017-9882-4

Aspectos probabilísticos y geométricos de la teoría de funciones
Nicolau Nos, A. (PI), Gonzalez Llorente, J. (Investigador/a Principal 2), Arroyo Garcia, A. R. (Col.laborador/a), Donaire Benito, J. J. (Investigador/a), González Fuentes, M. J. (Investigador/a), Levi, M. (Investigador/a), Soler Gibert, O. (Col.laborador/a), Limani, A. (Col.laborador/a) & Macia Medina, V. J. (Col.laborador/a)
Ministerio de Economía y Competitividad (MINECO)
1/01/18 → 30/09/22
Projecte: Projectes i Ajuts a la Recerca

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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.",

keywords = "Calder{\'o}n–Zygmund operators, Generalized differences, H{\"o}lder functions, Law of the iterated logarithm, Lipschitz functions, Martingales, Oscillation, Zygmund class",

author = "Castro, {Alejandro J.} and Llorente, {Jos{\'e} G.} and Artur Nicolau",

year = "2018",

month = apr,

day = "1",

doi = "10.1007/s12220-017-9882-4",

language = "English",

volume = "28",

pages = "1665--1686",

journal = "Journal of Geometric Analysis",

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number = "2",

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TY - JOUR

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

SN - 1050-6926

VL - 28

SP - 1665

EP - 1686

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 2

ER -

Oscillation of Generalized Differences of Hölder and Zygmund Functions

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Aspectos probabilísticos y geométricos de la teoría de funciones

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