Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Hausdorff measure

Sortuj według:

Ogranicz wyniki do:

A Fourier analytical characterization of the Hausdorff dimension of a closed set and of related Lebesgue spaces

100%

Triebel H., Winkelvoss H.

Studia Mathematica

1996

tom 121

nr 2

149-166

Let Γ be a closed set in $ℝ^n$ with Lebesgue measure |Γ| = 0. The first aim of the paper is to give a Fourier analytical characterization of Hausdorff dimension of Γ. Let 0 < d < n. If there exist a Borel measure µ with supp µ ⊂ Γ and constants $c_{1} > 0$ and $c_{2} > 0$ such that $c_{1}r^{d} ≤ µ (B(x,r)) ≤ c_{2}r^{d}$ for all 0 < r < 1 and all x ∈ Γ, where B(x,r) is a ball with centre x and radius r, then Γ is called a d-set. The second aim of the paper is to provide a link between the related Lebesgue spaces $L_{p}(Γ)$, 0 < p ≤ ∞, with respect to that measure µ on the hand and the Fourier analytically defined Besov spaces $B^s_{p,q}(ℝ^n)$ (s ∈ ℝ, 0 < p ≤ ∞, 0 < q ≤ ∞) on the other hand.

Blow-up of regular submanifolds in Heisenberg groups and applications

75%

Magnani V.

Open Mathematics

2006

tom 4

nr 1

82-109

We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence of currents. Another application is the proof of an intrinsic coarea formula for vector-valued mappings on the Heisenberg group.

Ograniczanie wyników

1 Open Mathematics

1 Studia Mathematica

1 Magnani V.

1 Triebel H.

1 Winkelvoss H.

1 2006

1 1996

Wyniki wyszukiwania

A Fourier analytical characterization of the Hausdorff dimension of a closed set and of related Lebesgue spaces

Blow-up of regular submanifolds in Heisenberg groups and applications