Weighted norm inequalities for strongly singular convolution operators

Abstract

We derive sharp function estimates for convolution operators whose kernels are more singular than Calderon-Zygmund kernels. This leads to weighted norm inequalities. Weighted weak <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis 1 comma 1 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(1,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> results are also proved. All the results obtained are in the context of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A Subscript p"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{A_p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> weights.

Locations

• Transactions of the American Mathematical Society - View - PDF