Abstract
Frisch-Parisi conjecture claims the existence of Baire function spaces in which Baire typical functions share the same multifractal behavior, prescribed in advance, and obey a multifractal formalism. In this paper, we introduce a family B of heterogeneous Besov spaces, which generalize the standard Besov spaces - they are obtained by replacing the Lebesgue measure (which plays a key role in the definition of the standard Besov spaces) by multifractal Radon measures belonging to some class constructed in the companion paper [1]. We find a characterization of the elements of B in terms of wavelet coefficients, and then describe the multifractal properties (singularity spectrum, validity of the multifractal formalism) of their Baire typical functions. This allows us to fully solve the Frisch-Parisi conjecture inside B.
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