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See detailSome Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in T_p^\alpha(x)
Loosveldt, Laurent UL; Nicolay, Samuel

in Journal of Fourier Analysis and Applications (2022), 28(4),

We present prevalent results concerning generalized versions of the $T_p^\alpha$ spaces, initially introduced by Calderón and Zygmund. We notably show that the logarithmic correction appearing in the ... [more ▼]

We present prevalent results concerning generalized versions of the $T_p^\alpha$ spaces, initially introduced by Calderón and Zygmund. We notably show that the logarithmic correction appearing in the quasi-characterization of such spaces is mandatory for almost every function; it is in particular true for the Hölder spaces, for which the existence of the correction was showed necessary for a specific function. We also show that almost every function from $T_p^α (x0 )$ has α as generalized Hölder exponent at $x_0$. [less ▲]

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