Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms

M. Wojciechowski

Studia Mathematica (1991)

  • Volume: 100, Issue: 2, page 149-167
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Wojciechowski, M.. "Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms." Studia Mathematica 100.2 (1991): 149-167. <http://eudml.org/doc/215879>.

@article{Wojciechowski1991,
abstract = {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.},
author = {Wojciechowski, M.},
journal = {Studia Mathematica},
keywords = {translation invariant projections; Sobolev spaces; norm},
language = {eng},
number = {2},
pages = {149-167},
title = {Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms},
url = {http://eudml.org/doc/215879},
volume = {100},
year = {1991},
}

TY - JOUR
AU - Wojciechowski, M.
TI - Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms
JO - Studia Mathematica
PY - 1991
VL - 100
IS - 2
SP - 149
EP - 167
AB - 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.
LA - eng
KW - translation invariant projections; Sobolev spaces; norm
UR - http://eudml.org/doc/215879
ER -

References

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  1. [C] P. J. Cohen, On a conjecture of Littlewood and idempotent measures, Amer. J. Math. 82 (1960), 191-212. Zbl0099.25504
  2. [G-McG] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, 1979. Zbl0439.43001
  3. [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. Zbl0435.43002
  4. [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. Zbl0473.42001
  5. [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. Zbl0679.46024
  6. [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. Zbl0628.46027
  7. [P-W] A. Pełczyński and M. Wojciechowski, to appear. 
  8. [W] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Univ. Press, 1990. Zbl0858.46002

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