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arXiv · 1303.6521

Estimates for Nonlinear Harmonic Measures on Trees

Leandro M. Del Pezzo·Carolina A. Mosquera·Julio D. Rossi
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Abstract

In this paper we give some estimates for nonlinear harmonic measures on trees. In particular, we estimate in terms of the size of a set $D$ the value at the origin of the solution to $ u(x)=F((x,0),\dots,(x,m-1))$ for every $x\in\mathbb{T}_m, $ a directed tree with $m$ branches with initial datum $f+\chi_D$. Here $F$ is an averaging operator on $\mathbb{R}^m$, $x$ is a vertex of a directed tree $\mathbb{T}_m$ with regular $m$-branching and $(x,i)$ denotes a successor of that vertex for $0\le i\le m-1$.

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Leandro M. Del Pezzo, Carolina A. Mosquera, Julio D. Rossi. 2013-03-26. Estimates for Nonlinear Harmonic Measures on Trees. https://doi.org/10.1007/s00574-014-0056-8

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