We characterize those anisotropic Sobolev spaces on tori in the and uniform norms for which the idempotent multipliers have a description in terms of the coset ring of the dual group. These results are deduced from more general theorems concerning invariant projections on vector-valued function spaces on tori. This paper is a continuation of the author’s earlier paper [W].
@article{bwmeta1.element.bwnjournal-article-smv104i2p181bwm,
author = {M. Wojciechowski},
title = {Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {181-193},
zbl = {0810.46031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv104i2p181bwm}
}
Wojciechowski, M. Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections. Studia Mathematica, Tome 104 (1993) pp. 181-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv104i2p181bwm/
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[00001] [P-W1] A. Pełczyński and M. Wojciechowski, Paley projections on anisotropic Sobolev space on tori, Proc. London Math. Soc. 65 (2) (1992), 405-422. | Zbl 0767.46033
[00002] [P-W2] A. Pełczyński and M. Wojciechowski, Translation invariant projections on anisotropic Sobolev spaces on tori; a survey, to appear. | Zbl 0811.46027
[00003] [W] M. Wojciechowski, Translation invariant projections in Sobolev spaces on tori in the and uniform norms, Studia Math. 100 (2) (1991), 149-167. | Zbl 0759.46017