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Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

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García-Cuerva J., Kazarian K. S.

Studia Mathematica

1994

tom 109

nr 3

255-276

We study sufficient conditions on the weight w, in terms of membership in the $A_p$ classes, for the spline wavelet systems to be unconditional bases of the weighted space $H^p(w)$. The main tool to obtain these results is a very simple theory of regular Calderón-Zygmund operators.

Quantized orthonormal systems: A non-commutative Kwapień theorem

100%

García-Cuerva J., Parcet J.

Studia Mathematica

2003

tom 155

nr 3

273-294

The concepts of Riesz type and cotype of a given Banach space are extended to a non-commutative setting. First, the Banach space is replaced by an operator space. The notion of quantized orthonormal system, which plays the role of an orthonormal system in the classical setting, is then defined. The Fourier type and cotype of an operator space with respect to a non-commutative compact group fit in this context. Also, the quantized analogs of Rademacher and Gaussian systems are treated. All this is used to obtain an operator space version of the classical theorem of Kwapień characterizing Hilbert spaces by means of vector-valued orthogonal series. Several approaches to this result with different consequences are given.

Ograniczanie wyników

2 Studia Mathematica

2 García-Cuerva J.

1 Kazarian K. S.

1 Parcet J.

1 2003

1 1994

Wyniki wyszukiwania

Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

Quantized orthonormal systems: A non-commutative Kwapień theorem