A compactness criterion and application to the commutators associated with Schrödinger operators. Issue 2 (9th September 2014)

• Record Type: Journal Article
• Authors: Li, Pengtao; Mo, Yan; Zhang, Chuangyuan
• Is Part Of: Mathematische Nachrichten. Volume 288:Issue 2/3(2015)
• Page Start: 235
• Page End: 248
• Publication Date: 2014-09-09
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201300286
• Languages: English
• ISSNs: 0025-584X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>Let <italic>T</italic> be an integral operator. In this paper, we introduce a <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh3hv47zvt" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:dummy:media:mana201300286:mana201300286-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:math></alternatives></inline-formula>‐compactness criterion of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh3hv47zxx" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:dummy:media:mana201300286:mana201300286-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>[</mml:mo><mml:mi>b</mml:mi><mml:mo>, </mml:mo><mml:mi>T</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>, where <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh3hv47zwc" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:dummy:media:mana201300286:mana201300286-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>b</mml:mi><mml:mo>∈</mml:mo><mml:mtext mathvariant="italic">VMO</mml:mtext></mml:mrow></mml:math></alternatives></inline-formula>. As an application, we apply this criterion to deal with <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh3hv48001" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:dummy:media:mana201300286:mana201300286-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:math></alternatives></inline-formula>‐compactness of commutators associated to Schrödinger operators with potentials in the reverse Hölder's class.</p> </abstract>