Uniform minimality, unconditionality and interpolation in backward shift invariant subspaces

Eric Amar[1]; Andreas Hartmann[1]

  • [1] Université Bordeaux I Institut de Mathématiques Équipe d’Analyse & Géométrie 351 cours de la Libération 33405 Talence (France)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 6, page 1871-1903
  • ISSN: 0373-0956

Abstract

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We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of standard Hardy spaces (and of other scales of spaces), changing the size of the space seems necessary to deduce unconditionality or interpolation from uniform minimality. Such a change can take two directions: lowering the power of integration, or “increasing” the defining inner function (e.g. increasing the type in the case of Paley-Wiener space). Khinchin’s inequalities play a substantial role in the proofs of our main results.

How to cite

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Amar, Eric, and Hartmann, Andreas. "Uniform minimality, unconditionality and interpolation in backward shift invariant subspaces." Annales de l’institut Fourier 60.6 (2010): 1871-1903. <http://eudml.org/doc/116324>.

@article{Amar2010,
abstract = {We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of standard Hardy spaces (and of other scales of spaces), changing the size of the space seems necessary to deduce unconditionality or interpolation from uniform minimality. Such a change can take two directions: lowering the power of integration, or “increasing” the defining inner function (e.g. increasing the type in the case of Paley-Wiener space). Khinchin’s inequalities play a substantial role in the proofs of our main results.},
affiliation = {Université Bordeaux I Institut de Mathématiques Équipe d’Analyse & Géométrie 351 cours de la Libération 33405 Talence (France); Université Bordeaux I Institut de Mathématiques Équipe d’Analyse & Géométrie 351 cours de la Libération 33405 Talence (France)},
author = {Amar, Eric, Hartmann, Andreas},
journal = {Annales de l’institut Fourier},
keywords = {Uniform minimality; unconditional bases; model spaces; Paley-Wiener spaces; interpolation; one-component inner functions; interpolating sequence; Carleson condition; Carleson measures},
language = {eng},
number = {6},
pages = {1871-1903},
publisher = {Association des Annales de l’institut Fourier},
title = {Uniform minimality, unconditionality and interpolation in backward shift invariant subspaces},
url = {http://eudml.org/doc/116324},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Amar, Eric
AU - Hartmann, Andreas
TI - Uniform minimality, unconditionality and interpolation in backward shift invariant subspaces
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 6
SP - 1871
EP - 1903
AB - We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of standard Hardy spaces (and of other scales of spaces), changing the size of the space seems necessary to deduce unconditionality or interpolation from uniform minimality. Such a change can take two directions: lowering the power of integration, or “increasing” the defining inner function (e.g. increasing the type in the case of Paley-Wiener space). Khinchin’s inequalities play a substantial role in the proofs of our main results.
LA - eng
KW - Uniform minimality; unconditional bases; model spaces; Paley-Wiener spaces; interpolation; one-component inner functions; interpolating sequence; Carleson condition; Carleson measures
UR - http://eudml.org/doc/116324
ER -

References

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