Estimates for operator norms on weighted spaces and reverse Jensen inequalities

Abstract

We examine the dependence on the<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>norm of<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="w"><mml:semantics><mml:mi>w</mml:mi><mml:annotation encoding="application/x-tex">w</mml:annotation></mml:semantics></mml:math></inline-formula>of the operator norms of singular integrals, maximal functions, and other operators in<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript p Baseline left-parenthesis w right-parenthesis"><mml:semantics><mml:mrow><mml:mrow class="MJX-TeXAtom-ORD"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:annotation encoding="application/x-tex">{L^p}(w)</mml:annotation></mml:semantics></mml:math></inline-formula>. We also examine connections between some fairly general reverse Jensen inequalities and the<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>and<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R upper H Subscript p"><mml:semantics><mml:mrow><mml:mi>R</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mi>H</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:annotation encoding="application/x-tex">R{H_p}</mml:annotation></mml:semantics></mml:math></inline-formula>weight conditions.

Locations

• Transactions of the American Mathematical Society - View - PDF