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Strong factorization of operators defined on subspaces of analytic functions in lattices

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Abstract

It is shown that for every 2-concave Banach lattice X of measurable fuctions on the circle, the quotient space X/XA has cotype 2. Here XA denotes the subclass of X consisting of the boundary values of analytic functions. It is also shown that, under slight additional assumptions, a p-concave operator defined on XA factors through L pA = Hp and extends to X, provided that X is p-convex. Bibliography: 10 titles.

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    D. S. Anisimov

  2. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    S. V. Kislyakov

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  1. D. S. Anisimov
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  2. S. V. Kislyakov
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 5–16.

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Anisimov, D.S., Kislyakov, S.V. Strong factorization of operators defined on subspaces of analytic functions in lattices. J Math Sci 141, 1511–1516 (2007). https://doi.org/10.1007/s10958-007-0056-y

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  • DOI: https://doi.org/10.1007/s10958-007-0056-y

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