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Pointwise regularity associated with function spaces and multifractal analysis

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Jaffard S.

Banach Center Publications

2006

tom 72

nr 1

93-100

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.

Ograniczanie wyników

1 Banach Center Publications

1 Jaffard S.

1 2006

Wyniki wyszukiwania

Pointwise regularity associated with function spaces and multifractal analysis