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- W2017383707 abstract "Here we introduce the<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>n</mml:mi></mml:math>th weighted space on the upper half-plane<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>Π</mml:mi><mml:mo>+</mml:mo></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>∈</mml:mo><mml:mi>ℂ</mml:mi><mml:mo>:</mml:mo><mml:mtext>I</mml:mtext><mml:mtext>m</mml:mtext><mml:mtext> </mml:mtext><mml:mi>z</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math>in the complex plane<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>ℂ</mml:mi></mml:math>. For the case<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>, we call it the Zygmund-type space, and denote it by<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>𝒵</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>Π</mml:mi><mml:mo>+</mml:mo></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>. The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operator<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>φ</mml:mi></mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>φ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>from the Hardy space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mi>p</mml:mi></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>Π</mml:mi><mml:mo>+</mml:mo></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>on the upper half-plane, to the Zygmund-type space, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>φ</mml:mi></mml:math>is an analytic self-map of the upper half-plane." @default.
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- W2017383707 date "2009-01-01" @default.
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- W2017383707 title "Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane" @default.
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