@inbook{3782446dcccb44b7a124da2296f76e9b,

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: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT# 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",

isbn = "978-3-031-13850-8",

series = "Operator Theory: Advances and Applications",

publisher = "Springer",

pages = "463--476",

booktitle = "Operator Theory",

address = "Netherlands",

}