Let denote the usual Hardy space of analytic functions on the unit disc . We prove that for every function there exists a linear operator defined on which is simultaneously bounded from to and from to such that . Consequently, we get the following results :
1) is a Calderon-Mitjagin couple;
2) for any interpolation functor , we have , where
denotes the closed subspace of of all functions whose Fourier coefficients vanish on negative integers.
These results also extend to Hardy spaces associated to general rearrangement invariant spaces on the unit circle.
Soit l’espace de Hardy de fonctions analytiques dans le disque unité . On démontre dans cet article que pour chaque fonction il existe un opérateur linéaire , défini sur , qui est simultanément borné de dans et de dans , et tel que . Par conséquent, on obtient les résultats suivants :
1) est un couple de Calderón-Mitjagin;
2) pour tout foncteur d’interpolation , on a , où désigne le sous-espace fermé de des fonctions dont les coefficients de Fourier s’annulent sur l’ensemble des entiers négatifs.
Ces résultats s’étendent aussi aux espaces de Hardy associés aux espaces invariants par réarrangement sur le cercle unité.
@article{AIF_1992__42_4_875_0, author = {Xu, Quanhua}, title = {Notes on interpolation of {Hardy} spaces}, journal = {Annales de l'Institut Fourier}, pages = {875--889}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {42}, number = {4}, year = {1992}, doi = {10.5802/aif.1313}, zbl = {0760.46060}, mrnumber = {94e:46135a}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1313/} }
TY - JOUR AU - Xu, Quanhua TI - Notes on interpolation of Hardy spaces JO - Annales de l'Institut Fourier PY - 1992 SP - 875 EP - 889 VL - 42 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1313/ DO - 10.5802/aif.1313 LA - en ID - AIF_1992__42_4_875_0 ER -
Xu, Quanhua. Notes on interpolation of Hardy spaces. Annales de l'Institut Fourier, Volume 42 (1992) no. 4, pp. 875-889. doi : 10.5802/aif.1313. https://aif.centre-mersenne.org/articles/10.5802/aif.1313/
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