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• W2606038389 endingPage "459" @default.
• W2606038389 startingPage "431" @default.
• W2606038389 abstract "We consider the non-local operator of variable order as follows: begin{equation*} Lf(x)= int _{{mathbb {R}}^dsetminus {0}}big (f(x+z)-f(x)-langle nabla f(x),zrangle {mathbb {1}}_{{|z|le 1}}big )frac {n(x,z)}{|z|^{d+alpha (x)}} dz, end{equation*} where $alpha (x)in [alpha _0,alpha _2]$ for any $xin {mathbb {R}}^d$ and some constants $0<alpha _0le alpha _2<2$ and $n(x,z)$ is a positive Borel measurable function bounded from above and below. Under mild continuity conditions on $alpha (x)$ and $n(x,z)$, we establish the Hölder regularity for the associated semigroups. The proof is based on a new construction of the coupling by reflection for non-local operator $L$, and the results successfully apply to both stable-like processes in the sense of Bass and time-change of symmetric stable processes." @default.
• W2606038389 created "2017-04-28" @default.
• W2606038389 creator A5012676602 @default.
• W2606038389 creator A5031957615 @default.
• W2606038389 date "2018-07-05" @default.
• W2606038389 modified "2023-10-16" @default.
• W2606038389 title "Coupling by reflection and Hölder regularity for non-local operators of variable order" @default.
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• W2606038389 doi "https://doi.org/10.1090/tran/7259" @default.
• W2606038389 hasPublicationYear "2018" @default.
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