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Dilations associated to flat curves.

Stephen Wainger (1991)

Publicacions Matemàtiques

I would like to give an exposition of the recent work of Tony Carbery, Mike Christ, Jim Vance, David Watson and myself concerning Hilbert transforms and Maximal functions along curves in R2 [CCVWW].

Existence of large ε-Kronecker and FZI₀(U) sets in discrete abelian groups

Colin C. Graham, Kathryn E. Hare (2012)

Colloquium Mathematicae

Let G be a compact abelian group with dual group Γ and let ε > 0. A set E ⊂ Γ is a “weak ε-Kronecker set” if for every φ:E → there exists x in the dual of Γ such that |φ(γ)- γ(x)| ≤ ε for all γ ∈ E. When ε < √2, every bounded function on E is known to be the restriction of a Fourier-Stieltjes transform of a discrete measure. (Such sets are called I₀.) We show that for every infinite set E there exists a weak 1-Kronecker subset F, of the same cardinality as E, provided there are not “too many”...

Fractional cartesian products of sets

Ron C. Blei (1979)

Annales de l'institut Fourier

Let E be a subset of a discrete abelian group whose compact dual is G . E is exactly p -Sidon (respectively, exactly non- p -Sidon) when ( * ) C E ( G ) ∧ ⊂ ℓ r holds if and only if r ∈ [ p , ∞ ] (respectively, r ∈ ( p , ∞ ) ). E is said to be exactly Λ β (respectively, exactly non- Λ β ) if E has the property ( * * ) every f ∈ L E 2 ( G ) satisfies ∫ G exp ( λ | f | 2 / α &lt; ∞ , for all λ &gt; 0 , if and only if α ∈ [ β , ∞ ) (respectively, α ∈ ( β , ∞ ) ).In this paper, for every p ∈ [ 1 , 2 ) and β ∈ [ 1 , ∞ ) , we display sets which are exactly p -Sidon, exactly non- p -Sidon, exactly Λ β and exactly non- Λ β .

Currently displaying 41 – 60 of 150