Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Interpolation of weighted and vector-valued Hardy spaces


Authors: Serguei V. Kisliakov and Quan Hua Xu
Journal: Trans. Amer. Math. Soc. 343 (1994), 1-34
MSC: Primary 46E15; Secondary 42B30, 46E40, 46M35
MathSciNet review: 1236225
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Real and complex interpolation methods, when applied to the couple $ ({H^{{p_0}}}({E_0};{w_0}),{H^{{p_1}}}({E_1};{w_1}))$, give what is expected if $ {E_0}$ and $ {E_1}$ are quasi-Banach lattices of measurable functions satisfying certain mild conditions and if $ \log (w_0^{1/{p_0}}w_1^{ - 1/{p_1}}) \in {\text{BMO}}\,({w_0},{w_1}$ being weights on the unit circle). The last condition is in fact necessary. (It is expected, of course, that the resulting spaces coincide with the subspaces of analytic functions in the corresponding interpolation spaces for the couple $ ({L^{{p_0}}}({E_0};{w_0}),{L^{{p_1}}}({E_1};{w_1})).)$


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E15, 42B30, 46E40, 46M35

Retrieve articles in all journals with MSC: 46E15, 42B30, 46E40, 46M35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1236225-7
PII: S 0002-9947(1994)1236225-7
Keywords: Interpolation, Hardy space, Banach lattice, $ {A_p}$-weight, Hilbert transform, BMO
Article copyright: © Copyright 1994 American Mathematical Society