Weighted weak-type (1, 1) estimates for radial Fourier multipliers via extrapolation theory

Weighted weak-type (1, 1) estimates for radial Fourier multipliers via extrapolation theory

In this paper, we prove a weighted estimate for the Bochner–Riesz operator at the critical index that is stronger than the weak-type (1,1) for A 1 weights, in the sense that the latter can be obtained via extrapolation arguments from the former. In addition, this estimate can be transferred to avera...

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Veröffentlicht in:Journal d'analyse mathématique (Jerusalem) 2019-07, Vol.138 (1), p.83-105
Hauptverfasser: Carro, María J., Domingo-Salazar, Carlos
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Analysis
Dynamical Systems and Ergodic Theory
Extrapolation
Functional Analysis
Mathematics
Mathematics and Statistics
Multipliers
Partial Differential Equations
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Zusammenfassung:In this paper, we prove a weighted estimate for the Bochner–Riesz operator at the critical index that is stronger than the weak-type (1,1) for A 1 weights, in the sense that the latter can be obtained via extrapolation arguments from the former. In addition, this estimate can be transferred to averages in order to deduce weighted weak-type (1,1) results for general radial Fourier multipliers.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-019-0018-6