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\noindent\parbox{2.85cm}{\includegraphics*[keepaspectratio=true,scale=1.75]{BJMA.jpg}}
\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
Banach J. Math. Anal. 2 (2008), no. 2, 150--162\\
$\frac{\rule{4.55in}{0.05in}}{{}}$\\
{\footnotesize
\textcolor[rgb]{0.65,0.00,0.95}{\textsc{\textbf{\large{B}}anach
\textbf{\large{J}}ournal of \textbf{\large{M}}athematical
\textbf{\large{A}}nalysis}}\\
ISSN: 1735-8787 (electronic)\\
\textcolor[rgb]{0.00,0.00,0.84}{\textbf{http://www.math-analysis.org }}\\
$\frac{{}}{\rule{4.55in}{0.05in}}$}\\[.5in]}



\title[Mixed means over spheres]
{Mixed means for centered and uncentered  averaging operators over
spheres and related results}


\author{I. Peri\'c}
\address{Faculty of Food Technology and Biotechnology \\ University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia.}
\email{\textcolor[rgb]{0.00,0.00,0.84}{iperic@pbf.hr}}

\dedicatory{This paper is dedicated to Professor Josip Pe\v{c}ari\'c\\
\vspace{.5cm} {\rm Submitted by M. S. Moslehian}}

\subjclass[2000]{Primary 26D10; Secondary 26D15.}

\date{Received: 30 April 2008; Accepted: 5 July 2008.}

\keywords{Mixed means, integral power means, power weights, centered
and uncentered spheres, polar coordinates, Hardy's inequality,
Carleman's inequality, spherical maximal functions, lower bounds for
operator norms.}


\begin{abstract}
\noindent Mixed-mean inequalities for integral power means over
centered and uncentered spheres are proved. Therefrom we deduce the
Hardy type inequalities for corresponding averaging operators.
Moreover, we discuss estimates related to the spherical maximal
functions.
\end{abstract}


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