L1Estimates for Maximal Functions and Riesz Transform on Real Rank 1 Semisimple Lie Groups

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

LetGbe a real rank one semisimple Lie group andKa maximal compact subgroup ofG. Radial maximal operators for suitable dilations, the heat and Poisson maximal operators, and the Riesz transform, which act onK-bi-invariant functions onG, satisfy theLp-norm inequalities forp 1 and a weak typeL1estimate. In this paper, through the Fourier theories onRandGwe shall duplicate the Hardy spaceH1(R) to a subspaceH1 s(G) (s≥0) ofL1(G) and show that these operators are bounded fromH1 s(G) toL1(G).

Original languageEnglish
Pages (from-to)327-357
Number of pages31
JournalJournal of Functional Analysis
Volume157
Issue number2
DOIs
Publication statusPublished - 1998 Aug 20

Fingerprint

Riesz Transform
Semisimple Lie Group
Maximal Function
Maximal Operator
Norm Inequality
Dilation
Siméon Denis Poisson
Heat
Subgroup
Invariant
Operator

ASJC Scopus subject areas

  • Analysis

Cite this

L1Estimates for Maximal Functions and Riesz Transform on Real Rank 1 Semisimple Lie Groups. / Kawazoe, Takeshi.

In: Journal of Functional Analysis, Vol. 157, No. 2, 20.08.1998, p. 327-357.

Research output: Contribution to journalArticle

@article{cbe29ba38b4e4bdaa92124ec6e574759,
title = "L1Estimates for Maximal Functions and Riesz Transform on Real Rank 1 Semisimple Lie Groups",
abstract = "LetGbe a real rank one semisimple Lie group andKa maximal compact subgroup ofG. Radial maximal operators for suitable dilations, the heat and Poisson maximal operators, and the Riesz transform, which act onK-bi-invariant functions onG, satisfy theLp-norm inequalities forp 1 and a weak typeL1estimate. In this paper, through the Fourier theories onRandGwe shall duplicate the Hardy spaceH1(R) to a subspaceH1 s(G) (s≥0) ofL1(G) and show that these operators are bounded fromH1 s(G) toL1(G).",
author = "Takeshi Kawazoe",
year = "1998",
month = "8",
day = "20",
doi = "10.1006/jfan.1998.3256",
language = "English",
volume = "157",
pages = "327--357",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - L1Estimates for Maximal Functions and Riesz Transform on Real Rank 1 Semisimple Lie Groups

AU - Kawazoe, Takeshi

PY - 1998/8/20

Y1 - 1998/8/20

N2 - LetGbe a real rank one semisimple Lie group andKa maximal compact subgroup ofG. Radial maximal operators for suitable dilations, the heat and Poisson maximal operators, and the Riesz transform, which act onK-bi-invariant functions onG, satisfy theLp-norm inequalities forp 1 and a weak typeL1estimate. In this paper, through the Fourier theories onRandGwe shall duplicate the Hardy spaceH1(R) to a subspaceH1 s(G) (s≥0) ofL1(G) and show that these operators are bounded fromH1 s(G) toL1(G).

AB - LetGbe a real rank one semisimple Lie group andKa maximal compact subgroup ofG. Radial maximal operators for suitable dilations, the heat and Poisson maximal operators, and the Riesz transform, which act onK-bi-invariant functions onG, satisfy theLp-norm inequalities forp 1 and a weak typeL1estimate. In this paper, through the Fourier theories onRandGwe shall duplicate the Hardy spaceH1(R) to a subspaceH1 s(G) (s≥0) ofL1(G) and show that these operators are bounded fromH1 s(G) toL1(G).

UR - http://www.scopus.com/inward/record.url?scp=0002299895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002299895&partnerID=8YFLogxK

U2 - 10.1006/jfan.1998.3256

DO - 10.1006/jfan.1998.3256

M3 - Article

VL - 157

SP - 327

EP - 357

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -