If is a bounded function on , the multiplier with symbol (denoted by is defined by , . We give some conditions on ensuring the “interpolation inequality” (here and is between 0 and 1). In most cases considered fails to have stronger -regularity properties (e.g. fails to be of weak type (1,1)). The results are applied to prove that for many sets every positive sequence in can be majorized by the sequence for some continuous funtion with spectrum in .
Soit une fonction bornée sur ; on définit le multiplicateur avec un symbole (noté par ) par , . On étudie des conditions sur qui garantissent “l’inégalité interpolationnelle” (ici , est entre 0 et 1 et ne dépend pas de ). Cette inégalité exprime une sorte de régularité de sur . (Pour la plupart les multiplicateurs en question ne sont pas de type faible (1,1).) On utilise ces résultats pour démontrer qu’il y a bien des sous-ensembles de tels que chaque suite positive dans puisse être majorée par la suite pour une fonction continue dont le spectre soit inclus dans .
@article{AIF_1988__38_2_147_0, author = {Kislyakov, Serguei V.}, title = {Fourier coefficients of continuous functions and a class of multipliers}, journal = {Annales de l'Institut Fourier}, pages = {147--183}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {38}, number = {2}, year = {1988}, doi = {10.5802/aif.1138}, mrnumber = {89j:42004}, zbl = {0607.42004}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1138/} }
TY - JOUR AU - Kislyakov, Serguei V. TI - Fourier coefficients of continuous functions and a class of multipliers JO - Annales de l'Institut Fourier PY - 1988 SP - 147 EP - 183 VL - 38 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1138/ DO - 10.5802/aif.1138 LA - en ID - AIF_1988__38_2_147_0 ER -
%0 Journal Article %A Kislyakov, Serguei V. %T Fourier coefficients of continuous functions and a class of multipliers %J Annales de l'Institut Fourier %D 1988 %P 147-183 %V 38 %N 2 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1138/ %R 10.5802/aif.1138 %G en %F AIF_1988__38_2_147_0
Kislyakov, Serguei V. Fourier coefficients of continuous functions and a class of multipliers. Annales de l'Institut Fourier, Volume 38 (1988) no. 2, pp. 147-183. doi : 10.5802/aif.1138. http://www.numdam.org/articles/10.5802/aif.1138/
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