Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A limit-point criterion for a class of Sturm-Liouville operators defined in ${L^p}$ spaces

Author(s): R. C. Brown
Journal: Proc. Amer. Math. Soc. 132 (2004), 2273-2280.
MSC (2000): Primary 47E05, 34C11, 34B24; Secondary 34C10
Posted: March 25, 2004
MathSciNet review: 2052403
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Abstract: Using a recent result of Chernyavskaya and Shuster we show that the maximal operator determined by on $[a,\infty)$ , $a>-\infty$ , where $q\ge 0$ and the mean value of computed over all subintervals of $\mathbb{R}$ of a fixed length is bounded away from zero, shares several standard ``limit-point at $\infty$ " properties of the case. We also show that there is a unique solution of that is in all $L^p[a, \infty)$ , $p=[1,\infty]$ .

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