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Let be $q>p$ then $L^q(\Omega)\subset L^p(\Omega)$. I will be able to say that all $f \in L^q$, such that $q>1$, have a Fourier Transform?.

pdta:I asking this because I am read that exist Fourier transform only when $f \in L^1$ but $L^q \subset L^p$.

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    On which space are you working? With which measure?2012-10-30
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    In the Lebesgue space2012-10-30
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    And what is $\Omega$?2012-10-30
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    The inclusion between $L^p$ spaces is only valid for $\Omega$ with finite measure (in this case: the larger the exponent, the smaller the space). I think this is what @Davide Giraudo is after...2012-10-30
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    $\Omega$ is bounded2012-10-30
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    What is the definition of the Fourier transform? From this, we can find a sufficient condition for the itengral defining it exists.2012-10-30
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    I suggest you put the condition: $\Omega$ is bounded into the post.2012-12-21

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