Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms
Wojciechowski, M.
Studia Mathematica, Tome 100 (1991), p. 149-167 / Harvested from The Polish Digital Mathematics Library

The idempotent multipliers on Sobolev spaces on the torus in the L¹ and uniform norms are characterized in terms of the coset ring of the dual group of the torus. This result is deduced from a more general theorem concerning certain translation invariant subspaces of vector-valued function spaces on tori.

Publié le : 1991-01-01
EUDML-ID : urn:eudml:doc:215879
@article{bwmeta1.element.bwnjournal-article-smv100i2p149bwm,
     author = {M. Wojciechowski},
     title = {Translation invariant projections in Sobolev spaces on tori in the L$^1$ and uniform norms},
     journal = {Studia Mathematica},
     volume = {100},
     year = {1991},
     pages = {149-167},
     zbl = {0759.46017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv100i2p149bwm}
}
Wojciechowski, M. Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms. Studia Mathematica, Tome 100 (1991) pp. 149-167. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv100i2p149bwm/

[00000] [C] P. J. Cohen, On a conjecture of Littlewood and idempotent measures, Amer. J. Math. 82 (1960), 191-212. | Zbl 0099.25504

[00001] [G-McG] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, 1979. | Zbl 0439.43001

[00002] [K-P] S. Kwapień and A. Pełczyński, Absolutely summing operators and translation invariant spaces of functions on compact abelian groups, Math. Nachr. 94 (1980), 303-340. | Zbl 0435.43002

[00003] [McG-P-S] O. C. McGehee, L. Pigno and B. Smith, Hardy's inequality and the L¹ norm of exponential sums, Ann. of Math. 113 (1981), 613-618. | Zbl 0473.42001

[00004] [P] A. Pełczyński, Boundedness of the canonical projection for Sobolev spaces generated by finite families of linear differential operators, in: Analysis at Urbana, Vol. I, London Math. Soc. Lecture Note Ser. 137, Cambridge Univ. Press, 1989, 395-415. | Zbl 0679.46024

[00005] [P-S] A. Pełczyński and K. Senator, On isomorphisms of anisotropic Sobolev spaces with "classical Banach spaces" and a Sobolev type embedding theorem, Studia Math. 84 (1986), 196-215. | Zbl 0628.46027

[00006] [P-W] A. Pełczyński and M. Wojciechowski, to appear.

[00007] [W] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Univ. Press, 1990. | Zbl 0858.46002