Integrable Harmonic Functions on Symmetric Spaces of Rank One

Yaakov Ben Natan; Yitzhak Weit

doi:10.1006/jfan.1998.3337

Integrable Harmonic Functions on Symmetric Spaces of Rank One

Yaakov Ben Natan
, Yitzhak Weit

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

If f ∈L¹(dμ) is harmonic in the spaceG/K, whereμis a radial measure withμ(G/K)=1, we have, by the mean value propertyf=f*μ. Conversely, does this mean value property imply thatfis harmonic ? In this paper we give a new and natural proof of a result obtained by P. Ahern, A. Flores, W. Rudin (J. Funct. Anal.11(1993), 380-397) and A. Koranyi (Contemp. Math.191(1995), 107-116) and generalize their result by providing sufficient conditions for a finite set of radial measuresμ_ion a symmetric space of rank one for whichf*μ_i=fimply thatfis harmonic.

Original language	English
Pages (from-to)	141-149
Number of pages	9
Journal	Journal of Functional Analysis
Volume	160
Issue number	1
DOIs	https://doi.org/10.1006/jfan.1998.3337
State	Published - 1 Dec 1998

Bibliographical note

Funding Information:
* Sponsored by the Edmund Landau Center for research in Mathematical supported by the Minerva Foundation (Germany).

Keywords

Harmonic functions; mean value property; symmetric spaces of rank one

ASJC Scopus subject areas

Analysis

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10.1006/jfan.1998.3337

Cite this

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abstract = "If f ∈L1(dμ) is harmonic in the spaceG/K, whereμis a radial measure withμ(G/K)=1, we have, by the mean value propertyf=f*μ. Conversely, does this mean value property imply thatfis harmonic ? In this paper we give a new and natural proof of a result obtained by P. Ahern, A. Flores, W. Rudin (J. Funct. Anal.11(1993), 380-397) and A. Koranyi (Contemp. Math.191(1995), 107-116) and generalize their result by providing sufficient conditions for a finite set of radial measuresμion a symmetric space of rank one for whichf*μi=fimply thatfis harmonic.",

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AU - Ben Natan, Yaakov

AU - Weit, Yitzhak

N1 - Funding Information: * Sponsored by the Edmund Landau Center for research in Mathematical supported by the Minerva Foundation (Germany).

PY - 1998/12/1

Y1 - 1998/12/1

N2 - If f ∈L1(dμ) is harmonic in the spaceG/K, whereμis a radial measure withμ(G/K)=1, we have, by the mean value propertyf=f*μ. Conversely, does this mean value property imply thatfis harmonic ? In this paper we give a new and natural proof of a result obtained by P. Ahern, A. Flores, W. Rudin (J. Funct. Anal.11(1993), 380-397) and A. Koranyi (Contemp. Math.191(1995), 107-116) and generalize their result by providing sufficient conditions for a finite set of radial measuresμion a symmetric space of rank one for whichf*μi=fimply thatfis harmonic.

AB - If f ∈L1(dμ) is harmonic in the spaceG/K, whereμis a radial measure withμ(G/K)=1, we have, by the mean value propertyf=f*μ. Conversely, does this mean value property imply thatfis harmonic ? In this paper we give a new and natural proof of a result obtained by P. Ahern, A. Flores, W. Rudin (J. Funct. Anal.11(1993), 380-397) and A. Koranyi (Contemp. Math.191(1995), 107-116) and generalize their result by providing sufficient conditions for a finite set of radial measuresμion a symmetric space of rank one for whichf*μi=fimply thatfis harmonic.

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Integrable Harmonic Functions on Symmetric Spaces of Rank One

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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