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Lebesgue integration question

  1. May 4, 2010 #1
    I'm working through some old prelim problems, and one of them has me stumped:

    "For [itex]0 < \alpha < \beta < \infty[/itex], for which positive real numbers [itex]p[/itex] do we have

    \frac{1}{x^\alpha + x^\beta} \in L^p (0,\infty)
  2. jcsd
  3. May 4, 2010 #2
    Analyze separately how it behaves near 0 and near infinity.
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