Pointwise regularity associated with function spaces and multifractal analysis

Stéphane Jaffard. "Pointwise regularity associated with function spaces and multifractal analysis." Banach Center Publications 72.1 (2006): 93-100. <http://eudml.org/doc/282152>.

@article{StéphaneJaffard2006,
abstract = {The purpose of multifractal analysis of functions is to determine the Hausdorff dimensions of the sets of points where a function (or a distribution) f has a given pointwise regularity exponent H. This notion has many variants depending on the global hypotheses made on f; if f locally belongs to a Banach space E, then a family of pointwise regularity spaces $C^\{α\}_\{E\}(x₀)$ are constructed, leading to a notion of pointwise regularity with respect to E; the case $E = L^\{∞\}$ corresponds to the usual Hölder regularity, and $E = L^\{p\}$ corresponds to the $T^\{p\}_\{α\}(x₀)$ regularity of Calderón and Zygmund. We focus on the study of the spaces $T^\{p\}_\{α\}(x₀)$; in particular, we give their characterization in terms of a wavelet basis and show their invariance under standard pseudodifferential operators of order 0.},
author = {Stéphane Jaffard},
journal = {Banach Center Publications},
keywords = {Pointwise regularity with respect to a Banach space; multifractal analysis of function},
language = {eng},
number = {1},
pages = {93-100},
title = {Pointwise regularity associated with function spaces and multifractal analysis},
url = {http://eudml.org/doc/282152},
volume = {72},
year = {2006},
}

TY - JOUR
AU - Stéphane Jaffard
TI - Pointwise regularity associated with function spaces and multifractal analysis
JO - Banach Center Publications
PY - 2006
VL - 72
IS - 1
SP - 93
EP - 100
AB - The purpose of multifractal analysis of functions is to determine the Hausdorff dimensions of the sets of points where a function (or a distribution) f has a given pointwise regularity exponent H. This notion has many variants depending on the global hypotheses made on f; if f locally belongs to a Banach space E, then a family of pointwise regularity spaces $C^{α}_{E}(x₀)$ are constructed, leading to a notion of pointwise regularity with respect to E; the case $E = L^{∞}$ corresponds to the usual Hölder regularity, and $E = L^{p}$ corresponds to the $T^{p}_{α}(x₀)$ regularity of Calderón and Zygmund. We focus on the study of the spaces $T^{p}_{α}(x₀)$; in particular, we give their characterization in terms of a wavelet basis and show their invariance under standard pseudodifferential operators of order 0.
LA - eng
KW - Pointwise regularity with respect to a Banach space; multifractal analysis of function
UR - http://eudml.org/doc/282152
ER -