Morrey spaces on spaces of homogeneous type and estimates for □b and the Cauchy-Szegö projection

Hitoshi Arai, Takahiro Mizuhara

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

In this paper, we define an appropriate version of Morrey spaces for spaces of homogeneous type. As our main result, we give a sufficient condition for an operator to be bounded on the version of Morrey spaces (cf. Theorem 3.1 and Corollary 3.5). Moreover, using this result, we prove Morrey space estimates for various operators arising in harmonic analysis and complex analysis of several variables.

Original languageEnglish
Pages (from-to)5-20
Number of pages16
JournalMathematische Nachrichten
Volume185
Publication statusPublished - 1997 Dec 1
Externally publishedYes

Fingerprint

Space of Homogeneous Type
Morrey Space
Cauchy
Projection
Estimate
Complex Analysis
Harmonic Analysis
Several Variables
Operator
Corollary
Sufficient Conditions
Theorem

Keywords

  • Kohn Laplacian
  • Morrey spaces
  • Singular integrals

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Morrey spaces on spaces of homogeneous type and estimates for □b and the Cauchy-Szegö projection. / Arai, Hitoshi; Mizuhara, Takahiro.

In: Mathematische Nachrichten, Vol. 185, 01.12.1997, p. 5-20.

Research output: Contribution to journalArticle

@article{9ef8a9a94cb34fb98887c14f7d636013,
title = "Morrey spaces on spaces of homogeneous type and estimates for □b and the Cauchy-Szeg{\"o} projection",
abstract = "In this paper, we define an appropriate version of Morrey spaces for spaces of homogeneous type. As our main result, we give a sufficient condition for an operator to be bounded on the version of Morrey spaces (cf. Theorem 3.1 and Corollary 3.5). Moreover, using this result, we prove Morrey space estimates for various operators arising in harmonic analysis and complex analysis of several variables.",
keywords = "Kohn Laplacian, Morrey spaces, Singular integrals",
author = "Hitoshi Arai and Takahiro Mizuhara",
year = "1997",
month = "12",
day = "1",
language = "English",
volume = "185",
pages = "5--20",
journal = "Mathematische Nachrichten",
issn = "0025-584X",
publisher = "Wiley-VCH Verlag",

}

TY - JOUR

T1 - Morrey spaces on spaces of homogeneous type and estimates for □b and the Cauchy-Szegö projection

AU - Arai, Hitoshi

AU - Mizuhara, Takahiro

PY - 1997/12/1

Y1 - 1997/12/1

N2 - In this paper, we define an appropriate version of Morrey spaces for spaces of homogeneous type. As our main result, we give a sufficient condition for an operator to be bounded on the version of Morrey spaces (cf. Theorem 3.1 and Corollary 3.5). Moreover, using this result, we prove Morrey space estimates for various operators arising in harmonic analysis and complex analysis of several variables.

AB - In this paper, we define an appropriate version of Morrey spaces for spaces of homogeneous type. As our main result, we give a sufficient condition for an operator to be bounded on the version of Morrey spaces (cf. Theorem 3.1 and Corollary 3.5). Moreover, using this result, we prove Morrey space estimates for various operators arising in harmonic analysis and complex analysis of several variables.

KW - Kohn Laplacian

KW - Morrey spaces

KW - Singular integrals

UR - http://www.scopus.com/inward/record.url?scp=0031447178&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031447178&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031447178

VL - 185

SP - 5

EP - 20

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

ER -