Meaning of uniformly continuous in a function $K:L^p \rightarrow L^p$

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The function $K$ is defined as $K(f)(x)=\int_{\mathbb{R}^n}k(x,y)f(y)dy$ (with k previously defined). The thing is, I have some more hypotesis, and I'm asked to show that $K$ is uniformly continuous. The thing is that I'm having doubts about what this would mean.

It's that if $||f-g||_{L^p} < \delta$ then $||K(f) - K(g)||_{L^p} < \epsilon$?

It's that if $|x-y| < \delta$ then $|K(f)(x) - K(f)(y)| < \epsilon$?

Is any other?

Sorry if this seems like a stupid question