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In this paper, a nonlinear version of the Extrapolation Theorem is proved and, as a corollary, a nonlinear version of Grothendieck's Theorem is presented. Finally, we prove that if $ T:X\to H$ being a pointed metric space and $ T(0)=0$ $ T^\char93 \vert _{H^*}$-summing $ (1\le q<\infty)$ is Lipschitz 1-summing. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove that there exist measures $ d\mu(x)=\gamma(x)dx$ $ \gamma(x)=\gamma_{0}(\vert x\vert)$ $ \gamma_{0}$ $ \mathcal{M}_{\mu}$ does not map $ L^{p}_{\mu}(\mathbb{R}^{n})$ $ L^{p}_{\mu}(\mathbb{R}^{n})$. This result answers an open question of P. Sjögren and F. Soria. [ABSTRACT FROM AUTHOR]