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Oscillation of Functions in the Hölder Class. / Mozolyako, Pavel; Nicolau, Artur.

In: Potential Analysis, Vol. 55, No. 1, 01.06.2021, p. 53-74.

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

Harvard

Mozolyako, P & Nicolau, A 2021, 'Oscillation of Functions in the Hölder Class', Potential Analysis, vol. 55, no. 1, pp. 53-74. https://doi.org/10.1007/s11118-020-09849-1

APA

Mozolyako, P., & Nicolau, A. (2021). Oscillation of Functions in the Hölder Class. Potential Analysis, 55(1), 53-74. https://doi.org/10.1007/s11118-020-09849-1

Vancouver

Mozolyako P, Nicolau A. Oscillation of Functions in the Hölder Class. Potential Analysis. 2021 Jun 1;55(1):53-74. https://doi.org/10.1007/s11118-020-09849-1

Author

Mozolyako, Pavel ; Nicolau, Artur. / Oscillation of Functions in the Hölder Class. In: Potential Analysis. 2021 ; Vol. 55, No. 1. pp. 53-74.

BibTeX

@article{bd71df09423b4ba1a8e783c6e487a303,
title = "Oscillation of Functions in the H{\"o}lder Class",
abstract = "We study the size of the set of points where the α-divided difference of a function in the H{\"o}lder class Λα is bounded below by a fixed positive constant. Our results are obtained from their discrete analogues which can be stated in the language of dyadic martingales. Our main technical result in this setting is a sharp estimate of the Hausdorff measure of the set of points where a dyadic martingale with bounded increments has maximal growth.",
keywords = "Dyadic martingales, Hausdorff measure, H{\"o}lder class",
author = "Pavel Mozolyako and Artur Nicolau",
year = "2021",
month = jun,
day = "1",
doi = "10.1007/s11118-020-09849-1",
language = "English",
volume = "55",
pages = "53--74",
journal = "Potential Analysis",
issn = "0926-2601",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Oscillation of Functions in the Hölder Class

AU - Mozolyako, Pavel

AU - Nicolau, Artur

PY - 2021/6/1

Y1 - 2021/6/1

N2 - We study the size of the set of points where the α-divided difference of a function in the Hölder class Λα is bounded below by a fixed positive constant. Our results are obtained from their discrete analogues which can be stated in the language of dyadic martingales. Our main technical result in this setting is a sharp estimate of the Hausdorff measure of the set of points where a dyadic martingale with bounded increments has maximal growth.

AB - We study the size of the set of points where the α-divided difference of a function in the Hölder class Λα is bounded below by a fixed positive constant. Our results are obtained from their discrete analogues which can be stated in the language of dyadic martingales. Our main technical result in this setting is a sharp estimate of the Hausdorff measure of the set of points where a dyadic martingale with bounded increments has maximal growth.

KW - Dyadic martingales

KW - Hausdorff measure

KW - Hölder class

UR - http://www.scopus.com/inward/record.url?scp=85086783004&partnerID=8YFLogxK

U2 - 10.1007/s11118-020-09849-1

DO - 10.1007/s11118-020-09849-1

M3 - Article

AN - SCOPUS:85086783004

VL - 55

SP - 53

EP - 74

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

IS - 1

ER -

ID: 119108859