Self-similar measures pushed to non-degenerate curves satisfy optimal L^p-flattening estimates for their Fourier transforms, implying quantitative dimension improvement under convolution.
Bishop and Yuval Peres, Fractals in probability and analysis, Cambridge Studies in Advanced Mathematics, vol
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$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves
Self-similar measures pushed to non-degenerate curves satisfy optimal L^p-flattening estimates for their Fourier transforms, implying quantitative dimension improvement under convolution.