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- W1606359629 abstract "We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type. We prove that there exists a constant<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:math>such that on Bergman spaces<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mi>D</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>with<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>p</mml:mi><mml:mo><</mml:mo><mml:mi>d</mml:mi></mml:math>there appears the so-called “gain regularity.” The constant<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:math>depends on the minimum of the dimension and the codimension of the subvariety. This means that the space of functions which admit an extension to a function in the Bergman space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mi>D</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>is strictly larger than<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mi>D</mml:mi><mml:mo>∩</mml:mo><mml:mi>A</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:math>is a subvariety." @default.
- W1606359629 created "2016-06-24" @default.
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- W1606359629 date "2015-01-01" @default.
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- W1606359629 title "Gain of Regularity in Extension Problem on Convex Domains" @default.
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- W1606359629 doi "https://doi.org/10.1155/2015/295759" @default.
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