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On a Bellman function associated with the Chang–Wilson–Wolff theorem: a case study

On a Bellman function associated with the Chang–Wilson–Wolff theorem: a case study

The tail of distribution (i.e., the measure of the set <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace f greater-than-or-equal-to x right-brace"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mi>f</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mi>x</mml:mi> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\{f\ge x\}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) is estimated for those functions <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f"> <mml:semantics> …