Oscillation of functions in the Hölder class

Arturo Nicolau Nos; Pavel Mozolyako

doi:10.1007/s11118-020-09849-1

Oscillation of functions in the Hölder class

Arturo Nicolau Nos, Pavel Mozolyako

Departament de Matemàtiques

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

Resum

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.

Idioma original	Anglès
Pàgines (de-a)	53–74
Nombre de pàgines	22
Revista	Potential Analysis
Volum	55
Número	1
DOIs	https://doi.org/10.1007/s11118-020-09849-1
Estat de la publicació	Publicada - 2021

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10.1007/s11118-020-09849-1

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https://www.scopus.com/pages/publications/85086783004

Aspectos probabilísticos y geométricos de la teoría de funciones
Nicolau Nos, A. (Investigador/a principal), Gonzalez Llorente, J. (Co-Investigador/a Principal), 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), Fons Europeu de Desenvolupament Regional (FEDER)
1/01/18 → 30/09/22
Projecte: Projectes i Ajuts a la Recerca

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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.",

author = "\{Nicolau Nos\}, Arturo and Pavel Mozolyako",

year = "2021",

doi = "10.1007/s11118-020-09849-1",

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T1 - Oscillation of functions in the Hölder class

AU - Nicolau Nos, Arturo

AU - Mozolyako, Pavel

PY - 2021

Y1 - 2021

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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.

UR - https://www.scopus.com/pages/publications/85086783004

U2 - 10.1007/s11118-020-09849-1

DO - 10.1007/s11118-020-09849-1

M3 - Article

SN - 0926-2601

VL - 55

SP - 53

EP - 74

JO - Potential Analysis

JF - Potential Analysis

IS - 1

ER -

Oscillation of functions in the Hölder class

Resum

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Aspectos probabilísticos y geométricos de la teoría de funciones

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