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Suppose that $d\geq2$ and $\alpha\in(1,2)$.
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Bogdan, KrzysztofK. (1997). The boundary Harnack principle for the fractional Laplacian. Studia Math. 123 43–80
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Bogdan, K.K., Kulczycki, T.T. andNowak, AdamA. (2002). Gradient estimates for harmonic and q q -harmonic functions of symmetric stable processes. Illinois J. Math. 46 541–556
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Chen, Zhen-QingZ.-Q., Kim, PankiP. andSong, RenmingR. (2010). Heat kernel estimates for the Dirichlet fractional Laplacian. J. Eur. Math. Soc. (JEMS) 12 1307–1329
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Chen, Zhen-QingZ.-Q., Kim, PankiP. andSong, RenmingR. (2010). Two-sided heat kernel estimates for censored stable-like processes. Probab. Theory Related Fields 146 361–399
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Bogdan, K.K. andJakubowski, T.T. (2012). Estimates of the Green function for the fractional Laplacian perturbed by gradient. Potential Anal. 36 455–481
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Chen, Z. Q.Z. Q., Kim, P.P., Song, R.R. andVondraček, Z.Z. (2012). Boundary Harnack principle for Δ + Δ α / 2 \Delta+\Delta^{\alpha/2} . Trans. Amer. Math. Soc
2012
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