The type set for homogeneous singular measures on ℝ ³ of polynomial type

• Autorzy: E. Ferreyra , T. Godoy
• Języki publikacji: EN

Abstrakty

EN

Let φ:ℝ ² → ℝ be a homogeneous polynomial function of degree m ≥ 2, let μ be the Borel measure on ℝ ³ defined by $μ(E) = ∫_{D} χ_{E}(x,φ(x))dx$ with D = {x ∈ ℝ ²:|x| ≤ 1} and let $T_{μ}$ be the convolution operator with the measure μ. Let $φ = φ₁^{e₁} ⋯ φₙ^{eₙ}$ be the decomposition of φ into irreducible factors. We show that if $e_{i} ≠ m/2$ for each $φ_{i}$ of degree 1, then the type set $E_{μ}: = {(1/p,1/q) ∈ [0,1] × [0,1]: ||T_{μ}||_{p,q} < ∞}$ can be explicitly described as a closed polygonal region.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 106
• Numer: 2
• Strony: 161-175

Daty

wydano

2006

Twórcy

autor

E. Ferreyra

• FaMAF, Universidad Nacional de Córdoba and CIEM (UNC - CONICET), Ciudad Universitaria, 5000 Córdoba, Argentina

autor

T. Godoy

• FaMAF, Universidad Nacional de Córdoba and CIEM (UNC - CONICET), Ciudad Universitaria, 5000 Córdoba, Argentina

Identyfikatory

DOI

10.4064/cm106-2-1