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L^p spaces are not equivalent for infinite measure sets

  1. Dec 16, 2007 #1
    Find a function f such that f is in L^P(R) but not in L^Q(R) for p not equal to q, where R is the set of real numers.

    I'm guessing I need to find a function that only blows up when it is raised to the qth power, but I am having some difficulty proving this.
     
  2. jcsd
  3. Dec 16, 2007 #2

    morphism

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    Try finding some function f that's in L^1 but not in L^2. To make things easier, you can choose a compactly-supported f.
     
  4. Dec 16, 2007 #3

    quasar987

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    I suppose just f = sin would do!
     
  5. Dec 16, 2007 #4

    morphism

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    It wouldn't, because sin isn't in any L^p(R) space. :tongue2:
     
  6. Dec 16, 2007 #5

    quasar987

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    Oh, right!:blushing:
     
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