WEIGHTED POINTWISE HARDY INEQUALITIES PEKKA KOSKELA AND JUHA LEHRBÄCK Abstract. We show that the weighted Hardy inequality

|∇u|pdΩβ, where dΩ(x) = dist(x, ∂Ω), holds for all u ∈ C∞0 (Ω) even for certain (sharp) exponents β> p − 1 when the visual boundary of the domain Ω ⊂ Rn is sufficiently big. In the case of the usual von Koch snowflake domain the sharp bound is shown to be β < p − 2 + λ, where λ = log 4 / log 3. These results are based on new pointwise Hardy inequalities