On the Korányi spherical maximal function on Heisenberg groups
On the Korányi spherical maximal function on Heisenberg groups
Abstract We prove $$L^p\rightarrow L^q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>q</mml:mi> </mml:msup> </mml:mrow> </mml:math> estimates for the local maximal operator associated with dilates of the Kóranyi sphere in Heisenberg groups. These estimates are sharp up to endpoints and imply new bounds on sparse domination for …