Factorization and extrapolation of pairs of weights
Intermediate spaces and the complex method of interpolation for families of Banach spaces
Weighted inequalities through factorization.
In [4] P. Jones solved the question posed by B. Muckenhoupt in [7] concerning the factorization of Ap weights. We recall that a non-negative measurable function w on Rn is in the class Ap, 1 < p < ∞ if and only if the Hardy-Littlewood maximal operator is bounded on Lp(Rn, w). In what follows, Lp(X, w) denotes the class of all measurable functions f defined on X for...
Miguel de Guzmán y la teoría de diferenciación de integrales.
The φ-transform and wavelet characterizations of Herz-type spaces.
In this paper, the authors establish the phi-transform and wavelet characterizations for some Herz and Herz-type Hardy spaces by means of a local version of the discrete tent spaces at the origin.
Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform
We just published a paper showing that the properties of the shift invariant spaces, ⟨f⟩, generated by the translates by ℤⁿ of an f in L²(ℝⁿ) correspond to the properties of the spaces L²(𝕋ⁿ,p), where the weight p equals [f̂,f̂]. This correspondence helps us produce many new properties of the spaces ⟨f⟩. In this paper we extend this method to the case where the role of ℤⁿ is taken over by locally compact abelian groups G, L²(ℝⁿ) is replaced by a separable Hilbert space on which a unitary representation...
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