Lacunary maximal functions on homogeneous groups

被引：3

作者：

Sheri, Aswin Govindan ^{[1
]}

Hickman, Jonathan ^{[1
]}

Wright, James ^{[1
]}

机构：

[1] Sch Math, James Clerk Maxwell Bldg,Kings Bldg,Peter Guthrie, Edinburgh EH9 3FD, Scotland

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2024年 / 286卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Lacunary maximal function; Homogeneous group; Heisenberg group; Calderon-Zygmund theory; OPERATORS;

D O I：

10.1016/j.jfa.2023.110250

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We observe that classical arguments of Ricci-Stein can be used to prove Lp bounds for maximal functions associated to lacunary dilates of a fixed measure in the setting of homogeneous groups. This recovers some recent results on averages over Koranyi spheres and horizontal spherical averages of a type introduced by Nevo-Thangavelu. Moreover, the main theorem applies much more broadly and we explore its consequences through a variety of explicit examples.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：25

共 21 条

[1] SPHERICAL MEANS ON THE HEISENBERG GROUP: STABILITY OF A MAXIMAL FUNCTION ESTIMATE [J].

Anderson, Theresa C. ;

Cladek, Laura ;

Pramanik, Malabika ;

Seeger, Andreas .

JOURNAL D ANALYSE MATHEMATIQUE, 2021, 145 (01) :1-28

[2]

Bagchi S, 2021, NEW YORK J MATH, V27, P631

[3]

Beltran D, 2022, ANN SCUOLA NORM-SCI, V23, P501

[4]

Bentsen G, 2022, INDIANA U MATH J, V71, P819

[5] HILBERT-TRANSFORMS ALONG CURVES .1. NILPOTENT GROUPS [J].

CHRIST, M .

ANNALS OF MATHEMATICS, 1985, 122 (03) :575-596

[6]

Christ Michael, 1992, Lecture Notes

[7] MAXIMAL AND SINGULAR INTEGRAL-OPERATORS VIA FOURIER-TRANSFORM ESTIMATES [J].

DUOANDIKOETXEA, J ;

DEFRANCIA, JLR .

INVENTIONES MATHEMATICAE, 1986, 84 (03) :541-561

[8]

Folland GB., 1982, HARDY SPACES HOMOGEN

[9] ON THE FOURIER ANALYTIC STRUCTURE OF THE BROWNIAN GRAPH [J].

Fraser, Jonathan M. ;

Sahlsten, Tuomas .

ANALYSIS & PDE, 2018, 11 (01) :115-132

[10]

Fraser Robert, 2023, Adv. Math., V416, P23

← 1 2 3 →