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Decomposition systems for function spaces

G. Kyriazis (2003)

Studia Mathematica

Let Θ : = θ I e : e E , I D be a decomposition system for L ( d ) indexed over D, the set of dyadic cubes in d , and a finite set E, and let Θ ̃ : = Θ ̃ I e : e E , I D be the corresponding dual functionals. That is, for every f L ( d ) , f = e E I D f , Θ ̃ I e θ I e . We study sufficient conditions on Θ,Θ̃ so that they constitute a decomposition system for Triebel-Lizorkin and Besov spaces. Moreover, these conditions allow us to characterize the membership of a distribution f in these spaces by the size of the coefficients f , Θ ̃ I e , e ∈ E, I ∈ D. Typical examples of such decomposition systems...

Directional operators and mixed norms.

Javier Duoandikoetxea (2002)

Publicacions Matemàtiques

We present a survey of mixed norm inequalities for several directional operators, namely, directional Hardy-Littlewood maximal functions and Hilbert transforms (both appearing in the method of rotations of Calderón and Zygmund), X-ray transforms, and directional fractional operators related to Riesz type potentials with variable kernel. In dimensions higher than two several interesting questions remain unanswered.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential...

Discrete Hardy spaces

Santiago Boza, María Carro (1998)

Studia Mathematica

We study various characterizations of the Hardy spaces H p ( ) via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of H p ( ) given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.

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