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Displaying similar documents to “Ultrasymmetric sequence spaces in approximation theory.”

Generalized Lions-Peetre methods of constants and means and operator ideals.

Antonio Manzano, Mieczyslaw Mastylo (2007)

Collectanea Mathematica

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We establish results on interpolation of Rosenthal operators, Banach-Saks operators, Asplund operators and weakly compact operators by means of generalized Lions-Peetre methods of constants and means. Applications are presented for the K-method space generated by the Calderón-Lozanovskii space parameters.

Wiener amalgam spaces for the fundamental identity of Gabor analysis.

Hans G. Feichtinger, Franz Luef (2006)

Collectanea Mathematica

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In the last decade it has become clear that one of the central themes within Gabor analysis (with respect to general time-frequency lattices) is a duality theory for Gabor frames, including the Wexler-Raz biorthogonality condition, the Ron-Shen duality principle and the Janssen representation of a Gabor frame operator. All these results are closely connected with the so-called , which we derive from an application of Poisson's summation formula for the symplectic Fourier transform. The...

Rough Marcinkiewicz integral operators on product spaces.

Hussein M. Al-Qassem (2005)

Collectanea Mathematica

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In this paper, we study the Marcinkiewicz integral operators M on the product space R x R. We prove that M is bounded on L(R x R) (1< p < ∞) provided that h is a bounded radial function and Ω is a function in certain block space B (S x S) for some q > 1. We also establish the optimality of our condition in the sense that the space B (S x S) cannot be replaced by B (S x S) for any −1 < r < 0. Our results...