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Thread: parameter

  1. April 12th 2011, 04:58 PM #1
    surjective
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    parameter

    Hello,

    I have the following function:

    \begin{displaymath}f(x) = \left\{\begin{array}{lr}\frac{1}{\sqrt{x}} & : x \in [1,\infty[\\0 & : x \notin [1,\infty[\end{array}\right.\end{displaymath}

    How do I calculate the exact value of the parameter p \in [1,\infty[ so that f \in L^{p}(\mathbb{R})?
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  2. April 12th 2011, 11:52 PM #2
    Moo
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    Hello,

    Well just compute \displaystyle\int |f(x)|^p ~dx=\int_1^\infty \frac{1}{x^{1/2+p}} ~dx

    This is a Riemann-type integral and it converges iff \frac 12+p>1
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