@inbook{533f613ca61f496787dff6e88d5f5dc4,
title = "Toeplitz Operators with Non-trivial Kernels and Non-dense Ranges on Weak Hardy Spaces",
abstract = "The well known Coburn lemma can be stated as follows: a nonzero Toeplitz operator T(a) with symbol a∈ L∞ has a trivial kernel or a dense range on the Hardy space Hp with p ∈ (1, ∞). We show that an analogue of this result does not hold for the Hardy-Marcinkiewicz (weak Hardy) spaces Hp,∞ with p ∈ (1, ∞): there exist continuous nonzero functions a: Depending on p such that dim (Ker T(a) ) = ∞ and (Forumala Presented).",
keywords = "Blaschke product, Coburn{\textquoteright}s lemma, Hardy-Marcinkiewicz space, Kernel, Range, Toeplitz operator",
author = "Oleksiy Karlovych and Eugene Shargorodsky",
note = "Funding Information: Acknowledgments This work was supported by national funds through the FCT—Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) within the scope of the project UIDB/00297/2020 (Centro de Matem{\'a}tica e Aplica{\c c}{\~o}es). Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2022",
doi = "10.1007/978-3-031-13851-5_20",
language = "English",
series = "Operator Theory: Advances and Applications",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "463--476",
booktitle = "Operator Theory",
address = "Germany",
}