Radial $A_p$ weights with applications to the disc multiplier and the Bochner-Riesz operators
Javier DuoandikoetxeaAdela MoyuaOsane OruetxebarriaEdurne Seijo
42B15radial weightsdisc multiplierBochner-Riesz operatorsmixed norm estimates
A characterization of radial $A_p$ weights is given in terms of the weights in $A_p(0,+\infty)$. Together with a result of Mockenhaupt this allows to describe a large class of radial weights for the disc multiplier in terms of the $A_2$ class of Muckenhoupt. The class of weights is large enough so as to deduce mixed norm inequalities with weights in the radial direction using extrapolation. Similar results are obtained for the Bochner-Riesz operators and for the Littlewood-Paley square function built on characteristic functions of dyadic annuli.
Indiana University Mathematics Journal
2008
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10.1512/iumj.2008.57.3282
10.1512/iumj.2008.57.3282
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Indiana Univ. Math. J. 57 (2008) 1261 - 1282
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