Displaying similar documents to “On the radius of a set in a Hilbert space”

A note on the parabolic variation

Miroslav Dont (2000)

Mathematica Bohemica

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A condition for solvability of an integral equation which is connected with the first boundary value problem for the heat equation is investigated. It is shown that if this condition is fulfilled then the boundary considered is 1 2 -Holder. Further, some simple concrete examples are examined.

Volume ratios in L p -spaces

Yehoram Gordon, Marius Junge (1999)

Studia Mathematica

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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 ) .