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