2013/04/28 by Olivia Constantin, Constantin, Olivia, José Ángel Peláez +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.1304.7501
We obtain a complete characterization of the entire functions g such that\nthe integral operator (T_ g f)(z)=\∫0zf(\ζ) ,g'(\ζ) ,d\ζ is\nbounded or compact, on a large class of Fock spaces \F^\φp,\ninduced by smooth radial weights that decay faster than the classical Gaussian\none. In some respects, these spaces turn out to be significantly different than\nthe classical Fock spaces. Descriptions of Schatten class integral operators\nare also provided. En route, we prove a Littlewood-Paley formula for\n||\⋅||\F^\φp and we characterize the positive Borel\nmeasures for which \F^\φp\⊂ Lq(\μ), 0<p,q<\∞. In\naddition, we also address the question of describing the subspaces of\n\F^\φp that are invariant under the classical Volterra integral\noperator.\n