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

• Autorzy: M. Wojciechowski
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 42B15: Multipliers
• 46E40: Spaces of vector- and operator-valued functions
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 104
• Numer: 2
• Strony: 181-193

Daty

wydano

1993

otrzymano

1992-06-30

Twórcy

autor

M. Wojciechowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

• [K] I. Kessler, Semidempotent measures on abelian groups, Bull. Amer. Math. Soc. 73 (1967), 258-260.
• [P-W1] A. Pełczyński and M. Wojciechowski, Paley projections on anisotropic Sobolev space on tori, Proc. London Math. Soc. 65 (2) (1992), 405-422.
• [P-W2] A. Pełczyński and M. Wojciechowski, Translation invariant projections on anisotropic Sobolev spaces on tori; a survey, to appear.
• [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.