We propose and analyze a robust BPX preconditioner for the integral fractional Laplacian on bounded  domains. For either quasi-uniform grids or graded bisection grids, we show that the condition numbers of the resulting systems remain uniformly bounded with respect to both the number of levels and the fractional power  .
We propose and analyze a robust BPX preconditioner for the integral fractional Laplacian on bounded Lipschitz domains. For either quasi-uniform grids or graded bisection grids, we show that the condition numbers of the resulting systems remain uniformly bounded with respect to both the number of levels and the fractional power . The results apply also to the spectral and censored fractional Laplacians .
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Lipschitz
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. The results apply also to the spectral and censored fractional Laplacians