Maximal functions associated to a family of flat curves in lacunary directions

被引：0

作者：

Oh, Jeongtae ^{[1
]}

Kim, Joonil ^{[1
]}

机构：

[1] Yonsei Univ, Dept Math, Seoul 120749, South Korea

来源：

MATHEMATISCHE ZEITSCHRIFT | 2024年 / 306卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

HILBERT-TRANSFORMS; CONVEX CURVES; OPERATORS;

D O I：

10.1007/s00209-024-03430-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the maximal operator defined by M-gamma(a)(x1,x2)=supk is an element of Zsupr>012r integral r-r|f(x1-t,x2-ak gamma(t))|dt, where{(t,gamma(t))}is a convex curve anda=(ak)is a lacunary sequence. We observe that gamma ' doubling assumption does not imply to theLpboundedness ofMa gamma. However, underthe infinitesimally doubling condition on gamma ', we obtain theLpboundedness ofMa gamma for all1<p< infinity.

引用

页数：14

共 50 条

[31] Weighted estimates for maximal functions associated with finite type curves in R2
Manna, Ramesh
Shrivastava, Saurabh
Shuin, Kalachand
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2021, 205
[32] LP ESTIMATES FOR MAXIMAL FUNCTIONS AND HILBERT-TRANSFORMS ALONG FLAT CONVEX CURVES IN R2
CARLSSON, H
CHRIST, M
CORDOBA, A
DUOANDIKOETXEA, J
DEFRANCIA, JLR
VANCE, J
WAINGER, S
WEINBERG, D
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 14 (02) : 263 - 267
[33] L(P)-BOUNDEDNESS OF THE HILBERT TRANSFORM AND MAXIMAL-FUNCTION ASSOCIATED TO FLAT PLANE-CURVES
ZIESLER, S
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 122 (04) : 1035 - 1043
[34] WEAK ESTIMATES ON MAXIMAL FUNCTIONS WITH RECTANGLES IN CERTAIN DIRECTIONS
STROMBERG, JO
ARKIV FOR MATEMATIK, 1977, 15 (02): : 229 - 240
[35] Maximal functions associated to filtrations
Christ, M
Kiselev, A
JOURNAL OF FUNCTIONAL ANALYSIS, 2001, 179 (02) : 409 - 425
[36] More on quadratic functions and maximal Artin–Schreier curves
Nurdagül Anbar
Wilfried Meidl
Applicable Algebra in Engineering, Communication and Computing, 2015, 26 : 409 - 426
[37] Quadratic functions and maximal Artin-Schreier curves
Anbar, Nurdagul
Meidl, Wilfried
FINITE FIELDS AND THEIR APPLICATIONS, 2014, 30 : 49 - 71
[38] A new family of maximal curves over a finite field
Massimo Giulietti
Gábor Korchmáros
Mathematische Annalen, 2009, 343
[39] MAXIMAL RANKS AND INTEGER POINTS ON A FAMILY OF ELLIPTIC CURVES
Walsh, P. G.
GLASNIK MATEMATICKI, 2009, 44 (01) : 83 - 87
[40] A new family of maximal curves over a finite field
Giulietti, Massimo
Korchmaros, Gabor
MATHEMATISCHE ANNALEN, 2009, 343 (01) : 229 - 245

← 1 2 3 4 5 →