Examples of Λ(4) sets E and a graph structure in E x E

• Autorzy: Ivo Klemes
• Języki publikacji: EN

Abstrakty

EN

We construct examples of Λ(4) sets E ⊂ ℤ. The construction uses certain families of thin intervals ${I_k} = ℒ ≈ E. The Λ(4) property for E is obtained from the stronger result that $||f||_{4} ≤ c||(∑|f_{I_k}|^2)^{1/2}_||_{4}$ where $f̂$ is supported on $(⋃ I_k) ⋂ ℤ$ and $f_{I_k}$ is defined by $f̂_{I_k} = χ_{I_k}f̂$. The proof of the latter involves a graph structure defined in terms of ℒ × ℒ (which is essentially E × E).

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products
• 42B25: Maximal functions, Littlewood-Paley theory
• 05C99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 133
• Numer: 2
• Strony: 101-120

Daty

wydano

1999

otrzymano

1997-01-27

poprawiono

1998-06-15

Twórcy

autor

Ivo Klemes

• Department of Mathematics and Statistics, 805 Sherbrooke Street West, McGill University, Montréal, Québec, H3A 2K6 Canada

Bibliografia

• [H1] K. E. Hare and I. Klemes, A new type of Littlewood-Paley partition, Ark. Mat. 30 (1992), 297-309.
• [H2] K. E. Hare and I. Klemes, On permutations of lacunary intervals, Trans. Amer. Math. Soc. 347 (1995), 4105-4127.
• [R] W. Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203-227.