Abstract
It is shown that in many cases the subspaces of bianalytic functions in various lattices of measurable functions on the torus T2 behave under real interpolation precisely as their parent lattices. Some applications to free interpolation by Fourier coefficients of bounded bianalytic functions are considered. (Note different meanings of the word “interpolation”.)
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
J. Bourgain, Bilinear forms on H ∞ and bounded bianalytic functions, Trans. Amer. Math. Soc. 286 (1984), no. 1, 313–337.
S. Janson, Interpolation of subcouples and quotient couples, Ark. Mat. 31 (1993), 307–338.
J.-P. Kahane, Y. Katznelson, and K. de Leeuw, Sur les coéfficients de Fourier des fonctions continues, C. R. Acad. Sci. Paris, 285 (1977), 1001–1004.
S. V. Kislyakov, Fourier coefficients of boundary values of functions that are analytic in the disc and bidisc, Trudy Math. Inst. Steklov, 155 (1981), 77–94.
S. V. Kislyakov, Interpolation of H P -spaces: some recent developments, In: Function spaces, interpolation spaces, and related topics, Israel Mathematical Conference Proceedings, 13. Amer. Math. Soc., Providence, R.I., 1999.
S. V. Kislyakov, Bourgain’s analytic projection revisited, Proc. Amer. Math. Soc. (to appear).
S. V. Kislyakov and Q. Xu, Real interpolation and singular integrals, St. Pe-tersburg Math. J., 8 (1997), no. 4, 593–615.
G. Pisier, Interpolation between H P spaces and noncommutative generaliza-tions. I, Pacific J. Math., 155 (1992), no. 2, 341–368.
Q. Xu, Some properties of the quotient space L 1 (Td)/H 1(Dd), Illinois J. Math., 37 (1993), no. 3, 437–454.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Basel AG
About this paper
Cite this paper
Kislyakov, S. (2000). Interpolation Involving Bounded Bianalytic Functions. In: Havin, V.P., Nikolski, N.K. (eds) Complex Analysis, Operators, and Related Topics. Operator Theory: Advances and Applications, vol 113. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8378-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8378-8_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9541-5
Online ISBN: 978-3-0348-8378-8
eBook Packages: Springer Book Archive