Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    [tex]
    \frac{1}{x^\alpha + x^\beta} \in L^p (0,\infty)
    [/tex]
     
  2. jcsd
  3. May 4, 2010 #2
    Analyze separately how it behaves near 0 and near infinity.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook