Commutators of log-Dini-type parametric Marcinkiewicz operators on non-homogeneous metric measure spaces
Commutators of log-Dini-type parametric Marcinkiewicz operators on non-homogeneous metric measure spaces
Abstract Let $(\mathcal{X}, d, \mu )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> <mml:mo>)</mml:mo> </mml:math> be a non-homogeneous metric measure space, which satisfies the geometrically doubling condition and the upper doubling condition. In this paper, the authors prove the boundedness in $L^{p} (\mu )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> …