Abstract
The real and complex interpolation spaces for the classical Hardy spaces H1 and H∞ were determined in 1983 by P. W. Jones. Due to the analytic constraints the associated Marcinkiewicz decomposition gives rise to a delicate approximation problem for the L1 metric. Specifically for f ε Hp the size of (formula presented) needs to be determined for any λ ε R+: In the present paper we develop a new set of truncation formulae in order to obtain the Marcinkiewicz decomposition of (H1, H∞). We revisit the real and complex interpolation theory for Hardy spaces by examining our newly found formulae.
| Original language | English |
|---|---|
| Pages (from-to) | 141-155 |
| Number of pages | 15 |
| Journal | Colloquium Mathematicum |
| Volume | 158 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2019 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© Instytut Matematyczny PAN, 2019.
Funding
Acknowledgements. P.F.X.M. and P.Y. were supported by the Austrian Science foundation (FWF) Pr. Nr. P28352 and P25591-N25, P29363-N32 respectively. P.F.X.M. and P.Y. were supported by the Austrian Science Foundation (FWF) Pr. Nr. P28352 and P25591-N25, P29363-N32 respectively.
| Funders | Funder number |
|---|---|
| Austrian Science Foundation | |
| Austrian Science Fund | P29363-N32, P28352, P25591-N25 |
Keywords
- Complex and real interpolation spaces
- Hardy spaces
- Holomorphic martingales
- Marcinkiewicz decomposition