Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections

M. Wojciechowski

Studia Mathematica (1993)

  • Volume: 104, Issue: 2, page 181-193
  • ISSN: 0039-3223

Abstract

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We characterize those anisotropic Sobolev spaces on tori in the L 1 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].

How to cite

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Wojciechowski, M.. "Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections." Studia Mathematica 104.2 (1993): 181-193. <http://eudml.org/doc/215968>.

@article{Wojciechowski1993,
abstract = {We characterize those anisotropic Sobolev spaces on tori in the $L^1$ 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].},
author = {Wojciechowski, M.},
journal = {Studia Mathematica},
keywords = {anisotropic Sobolev spaces on tori; idempotent multipliers; coset ring of the dual; invariant projections on vector-valued function spaces on tori},
language = {eng},
number = {2},
pages = {181-193},
title = {Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections},
url = {http://eudml.org/doc/215968},
volume = {104},
year = {1993},
}

TY - JOUR
AU - Wojciechowski, M.
TI - Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections
JO - Studia Mathematica
PY - 1993
VL - 104
IS - 2
SP - 181
EP - 193
AB - We characterize those anisotropic Sobolev spaces on tori in the $L^1$ 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].
LA - eng
KW - anisotropic Sobolev spaces on tori; idempotent multipliers; coset ring of the dual; invariant projections on vector-valued function spaces on tori
UR - http://eudml.org/doc/215968
ER -

References

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  1. [K] I. Kessler, Semidempotent measures on abelian groups, Bull. Amer. Math. Soc. 73 (1967), 258-260. Zbl0169.46202
  2. [P-W1] A. Pełczyński and M. Wojciechowski, Paley projections on anisotropic Sobolev space on tori, Proc. London Math. Soc. 65 (2) (1992), 405-422. Zbl0767.46033
  3. [P-W2] A. Pełczyński and M. Wojciechowski, Translation invariant projections on anisotropic Sobolev spaces on tori; a survey, to appear. Zbl0811.46027
  4. [W] M. Wojciechowski, Translation invariant projections in Sobolev spaces on tori in the L 1 and uniform norms, Studia Math. 100 (2) (1991), 149-167. Zbl0759.46017

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