Hokkaido Mathematical Journal

YABUTA Kōzō´,

A remark on radial ${A_p}$ weights.

Hokkaido Mathematical Journal, 40 (2011) pp.241-249

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Abstract

We show that a class of radial weights $\tilde A_p({\mathbb R}_+)$, introduced by Duoandikoetxea, is contained in the weight class $A_p^I({\mathbb R}^n)$ defined by using all $n$-dimensional rectangles with sides parallel to the coordinate axes.

MSC(Primary)42B20
MSC(Secondary)42B25, 47G10
Uncontrolled Keywords$A_p$ weights, singular integrals, $L^p$ boundedness, weighted norm inequalities, Marcinkiewicz integral