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We consider a family of Pomeau-Manneville type interval maps $T_\alpha$,parametrized by $\alpha \in (0,1)$, with the unique absolutely continuousinvariant probability measures $\nu_\alpha$, and rate of correlations decay$n^{1-1/\alpha}$. We show that despite the absence of a spectral gap for all$\alpha \in (0,1)$ and despite nonsummable correlations for $\alpha \geq 1/2$,the map $\alpha \mapsto \int \varphi \, d\nu_\alpha$ is continuouslydifferentiable for $\varphi \in L^{q}[0,1]$ for $q$ sufficiently large.

Linear response for intermittent maps with summable and nonsummable decay of correlations