Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Besov spaces in multifractal environment and the Frisch-Parisi
  conjecture   In this article, a solution to the so-called Frisch-Parisi conjecture is
brought. This achievement is based on three ingredients developed in this
paper. First almost-doubling fully supported Radon measures on $\R^d$ with a
prescribed singularity spectrum are constructed. Second we define new
\textit{heterogeneous} Besov spaces $B^{\mu,p}_{q}$ and find a characterization
using wavelet coefficients. Finally, we fully describe the multifractal nature
of typical functions in the function spaces $B^{\mu,p}_{q}$. Combining these
three results, we find Baire function spaces in which typical functions have a
prescribed singularity spectrum and satisfy a multifractal formalism. This
yields an answer to the Frisch-Parisi conjecture.

30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an