# Pointwise regularity associated with function spaces and multifractal analysis

Banach Center Publications (2006)

- Volume: 72, Issue: 1, page 93-100
- ISSN: 0137-6934

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topStéphane 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 -

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