given p>1, whats an example of f where $\int_{-\infty}^{\infty} |f| < \infty$ but $\int_{-\infty}^{\infty} |f|^p = \infty$
what about vica-versa? that is whats an example of g where $\int_{-\infty}^{\infty} |g| = \infty$ but $\int_{-\infty}^{\infty} |g|^p < \infty$