Abstract
The
t
-
multifractal formalism is a formula introduced by Jaffard and Mélot in order to deduce the
t
-
spectrum of a function
f
from the knowledge of the
(
p
,
t
)
-
oscillation exponent of
f
. The
t
-
spectrum is the Hausdorff dimension of the set of points where
f
has a given value of pointwise
L
t
regularity. The
(
p
,
t
)
-
oscillation exponent is measured by determining to which oscillation spaces
O
p
,
t
s
(defined in terms of wavelet coefficients)
f
belongs. In this paper, we first prove embeddings between oscillation and Besov-Sobolev spaces. We deduce a general lower bound for the
(
p
,
t
)
-
oscillation exponent. We then show that this lower bound is actually equality generically, in the sense of Baire’s categories, in a given Sobolev or Besov space. We finally investigate the Baire generic validity of the
t
-
multifractal formalism.