Hardy space estimates of Hausdorff operators on the Heisenberg group

被引：20

作者：

Wu, Qingyan ^{[1
]}

Fan, Dashan ^{[2
]}

机构：

[1] Linyi Univ, Dept Math, Linyi 276005, Shandong, Peoples R China

[2] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 164卷

基金：

中国国家自然科学基金;

关键词：

Hausdorff operator; Heisenberg group; Hardy space; Riesz transforms; Schrodinger representation; LITTLEWOOD AVERAGES; BOUNDEDNESS; BOUNDS;

D O I：

10.1016/j.na.2017.09.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This is a continuation of a series of works about Hausdorff operator on Hardy spaces in the setting of the Heisenberg group. In this paper, we obtain the boundedness from Lebesgue spaces to Hardy spaces for fractional Hausdorff operators and their compositions with Riesz transforms. We also establish the boundedness for two kinds of special Hausdorff operators, the Hausdorff-Poisson operator and the Hausdorff-Gauss operator, on Hardy spaces. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：135 / 154

页数：20

共 50 条

[21] The Weighted Lp estimates for the fractional Hardy operator and a class of integral operators on the Heisenberg group
He, Tianyang
Liu, Zhiwen
Yu, Ting
AIMS MATHEMATICS, 2025, 10 (01): : 858 - 883
[22] Hardy Type Estimates for Riesz Transforms Associated with Schrdinger Operators on the Heisenberg Group
Yu Liu
Guobin Tang
Analysis in Theory and Applications, 2016, 32 (01) : 78 - 89
[23] Compactness of commutators of Hardy operators on Heisenberg group
Xu, Jin
Zhao, Jiman
ADVANCES IN OPERATOR THEORY, 2024, 9 (04)
[24] Convolution operators and variable Hardy spaces on the Heisenberg group
Rocha, P.
ACTA MATHEMATICA HUNGARICA, 2024, 174 (02) : 429 - 452
[25] Weighted Hardy and Cesaro operators on Heisenberg group and their norms
Volosivets, S. S.
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2017, 28 (12) : 940 - 952
[26] HAUSDORFF OPERATORS ON HARDY SPACES
Liflyand, E.
EURASIAN MATHEMATICAL JOURNAL, 2013, 4 (04): : 101 - 141
[27] Lp and BMO bounds for weighted Hardy operators on the Heisenberg group
Chu, Jie Ying
Fu, Zun Wei
Wu, Qing Yan
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,
[28] Generalized Schrödinger operators on the Heisenberg group and Hardy spaces
Bui, The Anh
Hong, Qing
Hu, Guorong
JOURNAL OF FUNCTIONAL ANALYSIS, 2024, 286 (10)
[29] WEIGHTED MORREY ESTIMATES FOR HAUSDORFF OPERATOR AND ITS COMMUTATOR ON THE HEISENBERG GROUP
Ruan, Jianmiao
Fan, Dashan
Wu, Qingyan
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2019, 22 (01): : 307 - 329
[30] Weighted CBMO estimates for commutators of matrix Hausdorff operator on the Heisenberg group
Ajaib, Amna
Hussain, Amjad
OPEN MATHEMATICS, 2020, 18 : 496 - 511

← 1 2 3 4 5 →