Browsing by Subject "Haar system"

Now showing 1 - 3 of 3
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    Haar frame characterizations of Besov–Sobolev spaces and optimal embeddings into their dyadic counterparts
    (Springer, 2023) Garrigós Aniorte, Gustavo Adolfo; Seeger, Andreas; Ullrich, Tino; Matemáticas
    We study the behavior of Haar coefficients in Besov and Triebel-Lizorkin spaces on R , for a parameter range in which the Haar system is not an unconditional basis. First, we obtain a range of parameters, extending up to smoothness s<1, in which the spaces F(s,p,q) and B(s,p,q) are characterized in terms of doubly oversampled Haar coefficients (Haar frames). Secondly, in the case that 1/p
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    The Haar system in Triebel-Lizorkin spaces: endpoint results
    (Springer, 2021) Garrigós Aniorte, Gustavo Adolfo; Seeger, Andreas; Ullrich, Tino; Matemáticas
    We characterize the Schauder and unconditional basis properties for the Haar system in the Triebel-Lizorkin spaces F(s,p,q) in Rd, at the endpoint cases s=1 , s=d/p-d, and p=infty. Together with the earlier results in [10], [4], this completes the picture for such properties in the Triebel-Lizorkin scale, and complements a similar study for the Besov spaces given in [5].
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    The WCGA in Lp(logL)a spaces
    (Springer, 2023) Garrigós Aniorte, Gustavo Adolfo; Matemáticas
    We present new results concerning Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces X. First, we generalize a result of Temlyakov to cover situations in which the modulus of smoothness and the so called A3 parameter are not necessarily power functions. Secondly, we apply this new theorem to the Zygmund spaces Lp(log L)a , with 1