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• W1819744394 abstract "For a positive function <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> on the unit circle with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=log w element-of upper L Superscript 1> <mml:semantics> <mml:mrow> <mml:mi>log</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mi>w</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>log win L^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the following two statements are equivalent: (a) <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=log w element-of upper B upper M upper O> <mml:semantics> <mml:mrow> <mml:mi>log</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mi>w</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>B</mml:mi> <mml:mi>M</mml:mi> <mml:mi>O</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>log win BMO</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; (b) there is an operator <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Q> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding=application/x-tex>Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> projecting <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:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <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> onto <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Superscript p Baseline left-parenthesis w right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <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>H^p(w)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for all <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=1 greater-than p greater-than normal infinity> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>1>p>infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula> at once and having weak type (1,1) with respect to <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>." @default.
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• W1819744394 date "1998-01-01" @default.
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• W1819744394 title "Bourgain’s analytic projection revisited" @default.
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