Mateljević, M. Estimate for gradient, BMO and Lindelöf theorem. (English) Zbl 0944.31004 Publ. Inst. Math., Nouv. Sér. 58(72), 162-166 (1995). Let \(u_{\beta}\) denote the Bloch norm of a function \(u\in C^1(D)\), where \(D\) is a proper subdomain of \(\mathbb{R}^n\), and let \(u_*\) be its BMO norm.It is proved that if \(u\) is a harmonic function on \(D\) then \(u_{\beta}\leq (n+1) u_*\), and if \(u\in C^1(D)\), then \(u_*\leq b_n u_{\beta}\), where \(b_n=1+\frac 12+\cdots + \frac 1n\). Some applications of these estimates are given. Reviewer: Miroljub Jevtić (Beograd) MSC: 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions Keywords:Bloch norm; BMO norm; harmonic function PDFBibTeX XMLCite \textit{M. Mateljević}, Publ. Inst. Math., Nouv. Sér. 58(72), 162--166 (1995; Zbl 0944.31004) Full Text: EuDML