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

• Autorzy: M. Wojciechowski
• Języki publikacji: EN

Abstrakty

EN

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.

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: 1991
• Tom: 100
• Numer: 2
• Strony: 149-167

Daty

wydano

1991

otrzymano

1990-11-22

Twórcy

autor

M. Wojciechowski

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

Bibliografia

• [C] P. J. Cohen, On a conjecture of Littlewood and idempotent measures, Amer. J. Math. 82 (1960), 191-212.
• [G-McG] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, 1979.
• [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.
• [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.
• [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.
• [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.
• [P-W] A. Pełczyński and M. Wojciechowski, to appear.
• [W] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Univ. Press, 1990.