Polylogarithmic Hardy space & its Nevanlinna counting function
Functional Analysis
2021-10-22 v5
Abstract
We present the upper bound of the essential norm of the composition operator over the Polylogarithmic Hardy space PL2(D;s).The results involve the Nevanlinna counting function for PL2(D;s). We first prove the Littlewood-Paley Identity for PL2(D;s) which leads to the Nevanlinna counting function for PL2(D;s). With all these results, not only we get the upper bound of the essential norm of the composition operator over PL2(D;s) but also we get an upper bound in terms of the angular derivative and essential norm of composition operator over the Hardy space H2.
Keywords
Cite
@article{arxiv.2105.11597,
title = {Polylogarithmic Hardy space & its Nevanlinna counting function},
author = {Himanshu Singh},
journal= {arXiv preprint arXiv:2105.11597},
year = {2021}
}
Comments
Certain sections of the paper doesn't follow right explanation. Further investigation is needed