Displaying similar documents to “On the best constants in the Khinchin inequality”

Volume ratios in L p -spaces

Yehoram Gordon, Marius Junge (1999)

Studia Mathematica

Similarity:

There exists an absolute constant c 0 such that for any n-dimensional Banach space E there exists a k-dimensional subspace F ⊂ E with k≤ n/2 such that i n f e l l i p s o i d ε ⊂ B E ( v o l ( B E ) / v o l ( ε ) ) 1 / n ≤ c 0 i n f z o n o i d Z ⊂ B F ( v o l ( B F ) / v o l ( Z ) ) 1 / k . The concept of volume ratio with respect to ℓ p -spaces is used to prove the following distance estimate for 2 ≤ q ≤ p < ∞ : s u p F ⊂ ℓ p , d i m F = n i n f G ⊂ L q , d i m G = n d ( F , G ) ∼ c p q n ( q / 2 ) ( 1 / q - 1 / p ) .

New variants of Khintchine's inequality.

Ioan Serb (2001)

Collectanea Mathematica

Similarity:

Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.