Jevtić, Miroljub Growth of harmonic conjugates in the unit disc. (English) Zbl 0614.31001 Proc. Am. Math. Soc. 98, 41-45 (1986). Let \(M_p(r,u)\) be the usual \(p\)-mean of \(u(z)\) on \(| z| =r\). ”Assuming some mild regularity conditions on a positive nondecreasing function \(\psi(x)=O(x^a)\) for some \(a>0\), \(x\to \infty\), we show that \(M_p(r,u)=O(\psi (1/(1-r))\), \(r\to 1\), \(0<p<1\), implies \(M_p(r,v)=O\{\tilde{\psi}^p(1/(1-r))\}^{1/p}\), where \(u(z)+iv(z)\) is holomorphic in the open unit disc and \(\tilde{\psi}^p(x)=\int^{x}_{1/2}(\psi^ p(f)/f)\,dt\), \(x\geq\tfrac12.\)” Reviewer: Bo Kjellberg (Stockholm) Cited in 1 Document MSC: 31A05 Harmonic, subharmonic, superharmonic functions in two dimensions Keywords:harmonic conjugates; unit disc; mean; regularity; holomorphic PDFBibTeX XMLCite \textit{M. Jevtić}, Proc. Am. Math. Soc. 98, 41--45 (1986; Zbl 0614.31001) Full Text: DOI