Abstract
We develop a novel decomposition of the monomials in order to study the set of monomial convergence for spaces of holomorphic functions over for . For , the space of entire functions of bounded type in , we prove that is exactly the Marcinkiewicz sequence space , where the symbol is given by for .
For the space of -homogeneous polynomials on , we prove that the set of monomial convergence contains the sequence space , where . Moreover, we show that for any , the Lorentz sequence space lies in , provided that is large enough. We apply our results to make an advance in the description of the set of monomial convergence of (the space of bounded holomorphic functions on the unit ball of ). As a byproduct we close the gap on certain estimates related to the mixed unconditionality constant for spaces of polynomials over classical sequence spaces.
Citation
Daniel Galicer. Martín Mansilla. Santiago Muro. Pablo Sevilla-Peris. "Monomial convergence on ." Anal. PDE 14 (3) 945 - 984, 2021. https://doi.org/10.2140/apde.2021.14.945
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