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On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets

100%

Kwapień S., Sawa J.

Studia Mathematica

1993

tom 105

nr 2

173-187

The paper deals with the following conjecture: if μ is a centered Gaussian measure on a Banach space F,λ > 1, K ⊂ F is a convex, symmetric, closed set, P ⊂ F is a symmetric strip, i.e. P = {x ∈ F : |x'(x)| ≤ 1} for some x' ∈ F', such that μ(K) = μ(P) then μ(λK) ≥ μ(λP). We prove that the conjecture is true under the additional assumption that K is "sufficiently symmetric" with respect to μ, in particular it is true when K is a ball in Hilbert space. As an application we give estimates of Gaussian measures of large and small balls in a Hilbert space.

The best constant in the Khintchine inequality for complex Steinhaus variables, the case p=1

79%

Sawa J.

Studia Mathematica

1985

tom 81

nr 1

107-126

Ograniczanie wyników

2 Studia Mathematica

2 Sawa J.

1 Kwapień S.

1 1993

1 1985

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On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets

The best constant in the Khintchine inequality for complex Steinhaus variables, the case p=1