In this paper, we study the boundedness of commutator <mml:math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:math>
of Riesz transform associated with Schrödinger operator and b is BMO type
function, note that the kernel of T has no smoothness, and the boundedness from <mml:math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>H</mml:mi><mml:mi>b</mml:mi><mml:mn>1</mml:mn></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>→</mml:mo><mml:msup><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> is obtained.

Journal of Function Spaces

The boundedness of commutator of Riesz transform associated with Schrödinger operators on a Hardy space

Abstract

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