A new proof of an inequality of Littlewood and Paley
A new proof of an inequality of Littlewood and Paley
A fairly elementary new proof is presented of the inequality <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis p greater-than-or-equal-to 2 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(p \geq 2)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>: <disp-formula content-type="math/mathml"> \[ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral StartAbsoluteValue h Superscript prime Baseline EndAbsoluteValue …