Radial $A_p$ weights with applications to the disc multiplier and the Bochner-Riesz operators

Zuazo, Francisco Javier Duoandikoetxea; Pinillos, Adela Moyúa; Peña, Osane Oruetxebarria Fernández de la; Hernandorena, Edurne Seijo

doi:10.1512/iumj.2008.57.3282

Cited by 22 publications

(18 citation statements)

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“…Our third result extends the theory of limited range extrapolation to the weighted variable Lebesgue spaces. This concept was introduced by Auscher and Martell [5] and independently by Duoandikoetxea et al [28] in a somewhat different form. We generalize both their results.…”

Section: Main Theoremsmentioning

confidence: 99%

Extrapolation and weighted norm inequalities in the variable Lebesgue spaces

Cruz-Uribe

Lian

2016

Trans. Amer. Math. Soc.

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Abstract. We extend the theory of Rubio de Francia extrapolation, including offdiagonal, limited range and A ∞ extrapolation, to the weighted variable Lebesgue spaces L p(·) (w). As a consequence we are able to show that a number of different operators from harmonic analysis are bounded on these spaces. The proofs of our extrapolation results are developed in a way that outlines a general approach to proving extrapolation theorems on other Banach function spaces.

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Section: Main Theoremsmentioning

confidence: 99%

Extrapolation and weighted norm inequalities in the variable Lebesgue spaces

Cruz-Uribe

Lian

2016

Trans. Amer. Math. Soc.

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“…In Section 7 we consider another version of the extrapolation theorem, the limited-range extrapolation considered in [1] (and also to some extent in [10] and [18]). …”

Section: A Weight Is a Nonnegative Locally Integrable Function A Weimentioning

confidence: 99%

Extrapolation of weights revisited: New proofs and sharp bounds

Duoandikoetxea

2011

Journal of Functional Analysis

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111

110

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We use an appropriate factorization of the A p weights to give another proof of the extrapolation theorem of Rubio de Francia. It provides sharp bounds in terms of the A p -constant of the weights. Then we extend the result to more general settings including off-diagonal and partial range extrapolation. Among the applications, we prove by iteration a multivariable extrapolation theorem and give a sharp bound for Calderón-Zygmund operators on L p (w) for weights in A q (q < p).

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“…We need to remember that a radial weight function w ∈ A p (C d ) if and only if w(r ) ∈ A d−1 p (R + ), see [15]. Since S j (λ) also satisfies the weighted norm inequality for all λ ∈ R * , Theorem 1.2 can be proved in a similar way.…”

Section: Proposition 22 For Any K ∈ U (D) We Havementioning

confidence: 90%