Weighted norm inequalities for Bochner-Riesz operators and singular integral operators

Abstract

Weighted norm inequalities for the Bochner-Riesz operator at the critical index<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="one half left-parenthesis n minus 1 right-parenthesis"><mml:semantics><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:annotation encoding="application/x-tex">\frac {1}{2}(n - 1)</mml:annotation></mml:semantics></mml:math></inline-formula>are investigated. We also give some weighted norm inequalities for a class of singular integral operators introduced by Fefferman and Namazi.