On the Characterization of Triebel–Lizorkin Type Spaces of Analytic Functions

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Abstract

We consider different characterizations of Triebel–Lizorkin type spaces of analytic functions on the unit disc. Even though our results appear in the folklore, detailed descriptions are hard to find, and in fact we are unable to discuss the full range of parameters. Without additional effort we work with vector-valued analytic functions, and also consider a generalized scale of function spaces, including for example so-called Q-spaces. The primary aim of this note is to generalize, and clarify, a remarkable result by Cohn and Verbitsky, on factorization of Triebel–Lizorkin spaces. Their result remains valid for functions taking values in an arbitrary Banach space, provided that the vector-valuedness “sits in the right factor”. On the other hand, if we impose vector-valuedness on the “wrong” factor, then the factorization theorem fails even for functions taking values in a separable Hilbert space.

Detaljer

Författare
Externa organisationer
  • University of Leeds
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematisk analys

Nyckelord

Originalspråkengelska
Sidor (från-till)1491-1517
TidskriftJournal of Fourier Analysis and Applications
Volym24
Utgåva nummer6
Tidigt onlinedatum2017 dec 4
StatusPublished - 2018 dec
PublikationskategoriForskning
Peer review utfördJa