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Discrete Hardy spaces

Santiago BozaMaría 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.

From restricted type to strong type estimates on quasi-Banach rearrangement invariant spaces

María CarroLeonardo ColzaniGord Sinnamon — 2007

Studia Mathematica

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 T χ E X D ( | E | ) 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 | | f | | 1 , in the sense that T f X D ( | | f | | ) . 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...

On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity.

María Jesús Carro — 2002

Publicacions Matemàtiques

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... [check the paper abstract for the formula] This estimate implies that T: L log L → B, where B is a rearrangement invariant space. The purpose of this note is to give several characterizations...

Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates

María J. CarroElena Prestini — 2009

Studia Mathematica

We prove some extrapolation results for operators bounded on radial L p 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.

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