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\begin{document}
\setcounter{page}{94}

\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, 94--106\\
$\frac{\rule{4.55in}{0.05in}}{{}}$\\
{\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[On inequalities of Hardy--Sobolev type]{On inequalities of Hardy--Sobolev type}

\author[A. Balinsky, W.D. Evans, D. Hundertmark, R.T. Lewis]{A. Balinsky$^1$, W. D. Evans$^2$$^{*}$,
D. Hundertmark$^3$ and R. T. Lewis$^4$      }

\address{$^{1, 2}$ School of Mathematics, Cardiff University, 23 Senghennydd
Road, Cardiff CF24 4AG, UK.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{BalinskyA@cardiff.ac.uk} ,
\textcolor[rgb]{0.00,0.00,0.84}{EvansWD@cardiff.ac.uk}}

\address{$^{3}$ Department of Mathematics, University of Illinois at Urbana-Champaign,
1409 W. Green Street, Urbana, Illinois 61801,  USA.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{dirk@math.uiuc.edu}}

\address{$^{4}$ Department of Mathematics,
         University of Alabama at Birmingham,
         Birmingham, AL 35294-1170,
         USA.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{lewis@math.uab.edu}}


\dedicatory{This paper is dedicated to Professor Josip E. Pe\v{c}ari\'{c}\\
\vspace{.5cm} {\rm Submitted by T. Riedel}}


\subjclass[2000]{Primary 46E35; Secondary 35K05.}

\keywords{Hardy's inequality, Sobolev's inequality, heat semigroup,
Ledoux's inequality.}


\date{Received: 11 April; Accepted: 20 June 2008.
\newline \indent $^{*}$ Corresponding author}

\begin{abstract}
Hardy--Sobolev--type inequalities associated with the operator
$L:=\textbf{{x}} \cdot \nabla $ are established, using an
improvement to the Sobolev embedding theorem obtained by M.~Ledoux.
The analysis involves the determination of the operator semigroup
$\{e^{-tL^{*}L}\}_{t>0}.$
\end{abstract} \maketitle
\vspace{0.5in}
\end{document}

.
