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math.CA2024
Estimates for strongly singular operators along curves
Magali Folch-Gabayet, Ricardo A. Sáenz
For a proper function on the plane, we study the operator \[ Tf(x,y) = \lim_{\varepsilon\to 0} \int_\varepsilon^1 f(x-t,y-t^k) \frac{e^{2πi γ(t)}}{ψ(t)} dt, \] where an…
math.CA2013
Restrictions of harmonic functions and Dirichlet eigenfunctions of the Hata set to the interval
Baltazar Espinoza, Ricardo A. Sáenz
In this paper we study the harmonic functions and the Dirichlet eigenfunctions of the Hata set, and their restrictions to the interval , its main edge. We prove that these r…