Paper Title:

Sharp L^p Improving Results for Singular Measures on Cⁿ⁺¹

Author(s):

E. Ferreyra, M. Urciuolo

FaMAF-CIEM,
Universidad Nacional de Córdoba-Conicet,
Ciudad Universitaria, 5000 Córdoba,
Argentina

eferrey@famaf.unc.edu.ar
urciuolo@famaf.unc.edu.ar

Abstract:

For j=1,...,n, let Ω_j be open sets of the complex plane and let φ_j be holomorphic functions on Ω_j such that φ_j^'' does not vanish identically on Ω_j. We consider φ(z₁,...,z_n) =φ₁(z₁) +...+φ_n(z_n). We characterize the pairs (p,q) such that the convolution operator with the surface measure supported on a compact subset of the graph of φ is p-q bounded.

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