Heat Kernel Upper Estimates for Symmetric Jump Processes with Small Jumps of High Intensity

We consider the following non-local operator

$ \mathcal{A}f(x)=\lim\limits_{\varepsilon\to 0}\int_{\{y\in \mathbb{R}^d\colon |x-y|>\varepsilon\}}(f(y)-f(x))n(x,y)\,dh. $ \mathcal{A}f(x)=\lim\limits_{\varepsilon\to 0}\int_{\{y\in \mathbb{R}^d\colon |x-y|>\varepsilon\}}(f(y)-f(x))n(x,y)\,dh.
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