Vector-valued boundedness of harmonic analysis operators

Rutsky, Dmitry V.

doi:10.1090/spmj/1474

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And Hence They Admit Innerouter Factorization1

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Cited by 2 publications

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“…We will carry out some arguments based on a fixed point theorem applied to maps acting on sets of some majorants in lattices. In many cases it suffices to endow the sets of logarithms of such majorants with the weak topology of a weighted space L 2 (ω); see, e. g., [30,Proposition 30]. However, it is not clear if the convergence in this topology implies the convergence in τ , since in general log ω / ∈ L 1 in the first variable.…”

Section: And Hence They Admit Innerouter Factorizationmentioning

confidence: 99%

Real interpolation of Hardy-type spaces and BMO-regularity

Rutsky¹

2018

Preprint

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Let (X, Y ) be a couple of quasi-Banach lattices of measurable functions on T × Ω satisfying some additional assumptions. The K-closedness of a couple of Hardy-type spaces (X A , Y A ) in (X, Y ) and the stability of the real interpolation (X A , Y A ) θ,p = (X A + Y A ) ∩ (X, Y ) θ,p are shown to be equivalent to each other and to the BMO-regularity of the associated lattices L 1 , (X r ) ′ Y r δ,q . The inclusionis also characterized in these therms. New examples of couples (X A , Y A ) with this stability are given, proving that this property is strictly weaker than the BMOregularity of (X, Y ).

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Section: And Hence They Admit Innerouter Factorizationmentioning

confidence: 99%