Existence of L^q dimensions and entropy dimension for self-conformal measures

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Quantization (2019, unknown): “This work, along with Peres and Solomyak’s results on the L q -spectrum (cf. [23]), implies that, the quantization dimension for every self-similar measure on R q exists .”
Multifractal formalism for self-similar measures with weak separation condition (2009, unknown): “It was proved by Peres and Solomyak [30] that for any self-similar measure μ (without assuming any separation condition), the limit τ(q) = limr→0 logΘ(q;r) log r exists for q 0.”
Smoothness of the Lq‐Spectrum of Self‐Similar Measures with Overlaps (2003, methodology): “The relationship between τ(q )a nd the dimension of K(α )a s aboveis the well-known multifractal formalism .O nemay refer to [3, 18, 20 , 22 ]f or some further properties of the Lq-spectrum and multifractal formalism.”