On $M$-Bloch functions

Miroljub Jevti\'c and Miroslav Pavlovi\'c

Abstract: We define the class $M$, which contains eigenfunctions of the invariant Laplacian derivatives of $\Cal M$-harmonic functions, etc. For $f\in M$ we define $\|f\|_{\Cal B}$ and derive several quantities equivalent to $\|f\|_{\Cal B}$. Particularly, if $f$ is $\Cal M$-harmonic function, then $\|f\|_{\Cal B}$ is the usual Bloch norm. Higher-order derivatives characterisation of $\Cal M$-harmonic Bloch space is also given.

Classification (MSC2000): 32A37

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