We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for spaces and the recent method of Cobos-Peetre.
We show that the transference method of Coifman and Weiss can be extended to Hardy and Sobolev spaces. As an application we obtain the de Leeuw restriction theorems for multipliers.
We study various characterizations of the Hardy spaces via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.
Let X be a quasi-Banach rearrangement invariant space and let T be an (ε,δ)-atomic operator for which a restricted type estimate of the form for some positive function D and every measurable set E is known. We show that this estimate can be extended to the set of all positive functions f ∈ L¹ such that , in the sense that . This inequality allows us to obtain strong type estimates for T on several classes of spaces as soon as some information about the galb of the space X is known. In this paper...
Given a sublinear operator T satisfying that ||Tf||Lp(ν) ≤ C/(p-1) ||f||Lp(μ), for every 1 < p ≤ p0, with C independent of f and p, it was proved in [C] that...
We prove some extrapolation results for operators bounded on radial functions with p ∈ (p₀,p₁) and deduce some endpoint estimates. We apply our results to prove the almost everywhere convergence of the spherical partial Fourier integrals and to obtain estimates on maximal Bochner-Riesz type operators acting on radial functions in several weighted spaces.
We identify the intermediate space of a complex interpolation family -in the sense of Coifman, Cwikel, Rochberg, Sagher and Weiss- of L spaces with change of measure, for the complex interpolation method associated to any analytic functional.
We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega.
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