# Pointwise smoothness, two-microlocalization and wavelet coefficients.

Publicacions Matemàtiques (1991)

- Volume: 35, Issue: 1, page 155-168
- ISSN: 0214-1493

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topJaffard, Stéphane. "Pointwise smoothness, two-microlocalization and wavelet coefficients.." Publicacions Matemàtiques 35.1 (1991): 155-168. <http://eudml.org/doc/41681>.

@article{Jaffard1991,

abstract = {In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces Cx0s,s', and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet coefficients. We also give applications of these properties. In Part 2 some results on the microlocal spaces contained in [B2] will be recalled. Theorems 3 and 4 are also essentially contained in [B2]. The starting point for this paper was a note ([J1]) the author had written on a comparison between the Hölder criterion of regularity at a given point x0 and a corresponding property defined on the wavelet coefficients. Some easy proofs are omitted or abridged and can be found in [J2].},

author = {Jaffard, Stéphane},

journal = {Publicacions Matemàtiques},

keywords = {pointwise smoothness; two-microlocalization; wavelet coefficients; two- microlocal spaces; pseudodifferential operators},

language = {eng},

number = {1},

pages = {155-168},

title = {Pointwise smoothness, two-microlocalization and wavelet coefficients.},

url = {http://eudml.org/doc/41681},

volume = {35},

year = {1991},

}

TY - JOUR

AU - Jaffard, Stéphane

TI - Pointwise smoothness, two-microlocalization and wavelet coefficients.

JO - Publicacions Matemàtiques

PY - 1991

VL - 35

IS - 1

SP - 155

EP - 168

AB - In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces Cx0s,s', and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet coefficients. We also give applications of these properties. In Part 2 some results on the microlocal spaces contained in [B2] will be recalled. Theorems 3 and 4 are also essentially contained in [B2]. The starting point for this paper was a note ([J1]) the author had written on a comparison between the Hölder criterion of regularity at a given point x0 and a corresponding property defined on the wavelet coefficients. Some easy proofs are omitted or abridged and can be found in [J2].

LA - eng

KW - pointwise smoothness; two-microlocalization; wavelet coefficients; two- microlocal spaces; pseudodifferential operators

UR - http://eudml.org/doc/41681

ER -

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