On the Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^n × ℝ^m$, m ≥ 2

Ewa Ligocka

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We prove that, if μ>0, then there exists a linear manifold M of harmonic functions in $ℝ^{N}$ which is dense in the space of all harmonic functions in $ℝ^{N}$ and lim‖x‖→∞ x ∈ S ‖x‖μDαv(x) = 0 for every v ∈ M and multi-index α, where S denotes any hyperplane strip. Moreover, every nonnull function in M is universal. In particular, if μ ≥ N+1, then every function v ∈ M satisfies ∫H vdλ =0 for every (N-1)-dimensional hyperplane H, where λ denotes the (N-1)-dimensional Lebesgue measure. On the other...

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Displaying similar documents to “On the Hartogs-type series for harmonic functions on Hartogs domains in ℝ n × ℝ m , m ≥ 2”

Displaying similar documents to “On the Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^{n} \times ℝ^{m}$ , m ≥ 2”