Asymptotically Mean Value Harmonic Functions in Doubling Metric Measure Spaces-Reference-Cited by-同舟云学术

Asymptotically Mean Value Harmonic Functions in Doubling Metric Measure Spaces

Published:2022-01-01 Issue:1 Volume:10 Page:344-372
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:en
Short-container-title:

Author:

Adamowicz Tomasz¹,Kijowski Antoni²,Soultanis Elefterios³

Affiliation:

1. Institute of Mathematics, Polish Academy of Sciences , Warsaw , Poland

2. Analysis on Metric Spaces Unit, OIST , Okinawa , Japan

3. Radboud University , IMAPP , Nijmegen , The Netherlands

Abstract

Abstract We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds and in doubling metric measure spaces. We show that the strongly amv-harmonic functions are Hölder continuous for any exponent below one. More generally, we define the class of functions with finite amv-norm and show that functions in this class belong to a fractional Hajłasz–Sobolev space and their blow-ups satisfy the mean-value property. Furthermore, in the weighted Euclidean setting we find an elliptic PDE satisfied by amv-harmonic functions.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/agms-2022-0143/pdf

Reference39 articles.

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2. [2] T. Adamowicz, A. Kijowski, E. Soultanis, Asymptotically mean value harmonic functions in subriemannian and RCD settings, submitted.

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4. [4] J. M. Aldaz, Boundedness of averaging operators on geometrically doubling metric spaces Ann. Acad. Sci. Fenn. Math. 44(1) (2019), 497–503.

5. [5] A. Arroyo, J. Llorente, On the asymptotic mean value property for planar p-harmonic functions, Proc. Amer. Math. Soc. 144(9) (2016), 3859–3868.

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