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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, 42--58\\
$\frac{\rule{4.55in}{0.05in}}{{}}$\\
{\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
[Sum Inequalities in $\mathbf{L}^{\mathbf{p}}$ spaces]{Some weighted
sum and product inequalities in $\mathbf{L}^{\mathbf{p}}$ spaces and
their applications}
\author[R.C. Brown ]{R. C. Brown}

\address{Department of Mathematics, University
of Alabama-Tuscaloosa, AL 35487-0350, USA}
\email{\textcolor[rgb]{0.00,0.00,0.84}{dicbrown@bama.ua.edu}}
\dedicatory{This paper is dedicated to Professor Joseph E.
Pe\v{c}ari\'{c}\\ \vspace{.5cm} {\rm Submitted by Th. M. Rassias}}
 \subjclass[2000]{Primary: 26D10, 47A30, 34B24; Secondary
47E05}  \keywords{Weighted sum inequalities, weighted product
inequalities, Sturm Liouville operators, limit-point conditions,
relatively bounded perturbations}
\date{Received: 12 April 2008; Accepted 21 April 2008.}

\begin{abstract}
We survey some old and new results concerning weighted norm
inequalities of sum and product form and apply the theory to obtain
limit-point conditions for second order differential operators of
Sturm-Liouville form  defined in $L^p$ spaces. We also extend
results of Anderson and Hinton by giving necessary and sufficient
criteria that perturbations of such operators be relatively bounded.
Our work is in part a generalization of the classical Hilbert space
theory of Sturm-Liouville operators to a Banach space setting.
\end{abstract} \maketitle

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