P. Abry, S. Jaffard, and H. Wendt, Irregularities and scaling in signal and image processing: Multifractal analysis. Benoit Mandelbrot: A Life in Many Dimensions, World scientific publishing, pp.31-116, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00798427

J. Barral, Inverse problems in multifractal analysis of measures, Ann. Ec. Norm. Sup, vol.48, issue.6, pp.1457-1510, 2015.

J. Barral, F. B. Nasr, and J. Peyrière, Comparing multifractal formalisms: the neighboring condition, Asian J. Math, vol.7, pp.149-166, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00072026

J. Barral and A. Fan, On the estimation of the large deviations spectrum, Bull. Sci. Math, vol.144, issue.6, pp.1256-1283, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00747653

J. Barral and D. J. Feng, Multifractal formalism for almost all self-affine measures, Comm. Math. Phys, vol.318, pp.473-504, 2013.

J. Barral, N. Fournier, S. Jaffard, and S. Seuret, A pure jump Markov process with a random singularity spectrum, Ann. Probab, vol.38, issue.5, pp.1924-1946, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00693014

J. Barral and X. Jin, Multifractal analysis of complex random cascades, Comm. Math. Phys, vol.219, pp.129-168, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00790872

J. Barral and B. B. Mandelbrot, Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures (random multiplicative multifractal measures, part ii), Proc. Symp. Pures Math, vol.72, pp.17-52, 2004.

J. Barral and S. Seuret, The singularity spectrum of Lévy processes in multifractal time, Adv. Maths, vol.214, pp.149-166, 2007.

J. Barral and S. Seuret, Ubiquity and large intersections properties under digit frequencies constraints, Math. Proc. Cambridge Philos. Soc, vol.145, pp.527-548, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00693060

F. Bayart, Multifractal spectra of typical and prevalent measures, Nonlinearity, vol.26, pp.353-367, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00714388

F. Bayart and Y. Heurteaux, Multifractal analysis of the divergence of Fourier series, Ann. Sci. ENS, vol.45, pp.927-946, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00576918

G. Brown, G. Michon, and J. Peyrière, On the multifractal analysis of measures, J. Stat. Phys, vol.66, pp.775-790, 1992.

Z. Buczolich and J. Nagy, Hölder spectrum of typical monotone continuous functions. Real Anal. Exchange, pp.133-156, 1999.

Z. Buczolich and S. Seuret, Typical Borel measures on [0, 1] d satisfy a multifractal formalism, Nonlinearity, vol.23, issue.11, pp.7-13, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00693007

Z. Buczolich and S. Seuret, Measures and functions with prescribed singularity spectrum, J. Fractal Geometry, vol.1, issue.3, pp.295-333, 2014.

A. Cohen, Wavelet methods in numerical analysis, Handbook of Numerical Analysis, pp.417-711, 2000.

P. Collet, J. L. Lebowitz, and A. Porzio, The dimension spectrum of some dynamical systems, J. Stat. Phys, vol.47, pp.609-644, 1987.

I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure and App. Math, vol.41, pp.909-996, 1988.

A. Fan, J. Schmeling, and S. Troubetzkoy, A multifractal mass transference principle for Gibbs measures with applications to dynamical diophantine approximation, Proc. London Math. Soc, vol.107, issue.5, pp.1173-1219, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00150085

D. Feng, Gibbs properties of self-conformal measures and the multifractal formalism, Ergodic Theory Dynam, vol.27, pp.787-812, 2007.

D. J. Feng and K. S. Lau, Multifractal formalism for self-similar measures with weak separation condition, J. Math. Pures Appl, vol.92, pp.407-428, 2009.

U. Frisch and D. Parisi, Fully developed turbulence and intermittency in turbulence, and predictability in geophysical fluid dynamics and climate dynamics. International school of Physics "Enrico Fermi, vol.88, pp.84-88, 1985.

E. Gwynne, J. Miller, and X. Sun, Almost sure multifractal spectrum of schramm-loewner evolution, Duke Math. J, vol.167, issue.6, pp.1099-1237, 2017.

T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Fractal measures and their singularities: the characterisation of strange sets, Phys. Rev. A, vol.33, pp.1141-1151, 1986.

H. , Hentschel and I. Procaccia. The infinite number of generalized dimensions of fractals and strange attractors, Physica D, pp.435-444, 1983.

R. Hill and S. Velani, The ergodic theory of shrinking targets, Inv. Math, vol.119, pp.175-198, 1995.

R. Hill and S. Velani, The Jarnìk-Besicovitch theorem for geometrically finite Kleinian groups, Proc. Lond. Math. Soc, vol.77, pp.524-550, 1998.

R. Holley and E. C. Waymire, Multifractal dimensions and scaling exponents for strongly bounded random fractals, Ann. Appl. Probab, vol.2, pp.819-845, 1992.

X. Hu, J. Miller, and Y. Peres, Thick points of gaussian free fields, Ann. Probab, vol.38, issue.2, pp.896-926, 2010.

S. Jaffard, The spectrum of singularities of Riemann's function, Rev. Mat. Iberoamericana, vol.12, issue.2, pp.441-460, 1996.

S. Jaffard, Multifractal formalism for functions, Part 1: Results valid for all functions, Part 2: Selfsimilar functions, SIAM Journal of Mathematical Analysis, vol.28, issue.4, pp.944-998, 1997.

S. Jaffard, The multifractal nature of Lévy processes, Probab. Theory Related Fields, vol.114, issue.2, pp.207-227, 1999.

S. Jaffard, On the Frisch-Parisi conjecture, J. Math. Pures Appl, vol.79, issue.6, pp.525-552, 2000.

S. Jaffard, Wavelet techniques in multifractal analysis, Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot, Proc. Symposia in Pure Mathematic, 2004.

S. Jaffard and B. Martin, Multifractal analysis of the Brjuno function, Invent. Math, 2017.

S. Jaffard and Y. Meyer, On the pointwise regularity of functions in critical besov spaces, J. Func. Anal, vol.175, pp.415-434, 2000.

V. Jarnik, Diophantischen approximationen und Hausdorffsches mass, Mat. Sbornik, vol.36, pp.371-381, 1929.

J. F. King, The singularity spectrum for general Sierpinski carpets, Adv. Math, vol.116, pp.1-8, 1995.

K. S. Lau and S. Ngai, Multifractal measures and a weak separation condition, Adv. Math, vol.141, pp.45-96, 1999.

J. , L. Véhel, and R. Vojak, Multifractal analysis of Choquet capacities, Adv. Appl. Math, vol.20, pp.1-43, 1998.

N. G. Makarov, Fine structure of harmonic measure, St. Petersbourg Math. J, vol.10, pp.217-268, 1999.

B. B. Mandelbrot, Intermittent turbulence in self-similar cascades, divergence of high moments and dimension of the carrier, J. Fluid. Mech, vol.62, pp.331-358, 1974.

B. B. Mandelbrot, Multiplications aléatoires itérées et distributions invariantes par moyennes pondérées, C. R. Acad. Sci, vol.278, pp.289-292, 1974.

Y. Meyer, Ondelettes et opérateurs I. Hermann, 1990.

S. Ngai, A dimension result arising from the l q -spectrum of a measure, Proc. Amer. Math. Soc, vol.125, pp.2943-2951, 1997.

L. Olsen, A multifractal formalism, Adv. Math, vol.116, pp.92-195, 1995.

L. Olsen, Self-affine multifractal Sierpinski sponges in R d, Pacific J. Math, vol.183, pp.143-199, 1998.

S. Orey and S. J. Taylor, On the Hausdorff dimension of brownian slow points, Proc. London Math. Soc, vol.28, pp.174-192, 1974.

W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, vol.187, 1990.

E. Perkins, On the Hausdorff dimension of Brownian slow points, Z. Wahrscheinlichkeitstheorie verw. Gebiete, vol.64, pp.369-399, 1983.

Y. Pesin, Dimension theory in dynamical systems. Contemporary views and applications, 1997.

Y. Pesin, The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples, Chaos, vol.7, issue.89, 1997.

D. Rand, The singularity spectrum f (?) for cookie-cutters, Ergod. Th. Dynam. Sys, vol.9, pp.527-541, 1989.

R. Rhodes and V. Vargas, Gaussian multiplicative chaos and applications: A review, Probability surveys. IMS, vol.11, 2014.

S. Seuret and A. Ubis, Local L 2 -regularity of Riemann's Fourier series, Ann. Inst. Fourier, vol.67, issue.5, pp.2237-2264, 2017.

P. Shmerkin, On Furstenberg's intersection conjecture, self-similar measures, and the l q norms of convolutions, Ann. Math, vol.189, issue.2, pp.319-391, 2019.

H. Triebel, A note on wavelet bases in function spaces, Warsawa Institute of Mathematics of Polish Academy of Sciences, 2004.

F. J. Viklund and G. F. Lawler, Almost sure multifractal spectrum for the tip of an SLE curve, Acta Math, vol.209, issue.2, pp.265-322, 2012.

X. Yang, Multifractality of jump diffusion processes, Ann. Inst. Henri Poincaré Probab. Stat, vol.54, issue.4, pp.2042-2074, 2018.

J. Barral, C. Laga, I. Umr-7539, and . Galilée, LAMA (UMR, vol.13