On structure of discrete Muckenhoupt and discrete Gehring classes
On structure of discrete Muckenhoupt and discrete Gehring classes
Abstract In this paper, we study the structure of the discrete Muckenhoupt class $\mathcal{A}^{p}(\mathcal{C})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>A</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mo>(</mml:mo> <mml:mi>C</mml:mi> <mml:mo>)</mml:mo> </mml:math> and the discrete Gehring class $\mathcal{G}^{q}(\mathcal{K})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>G</mml:mi> <mml:mi>q</mml:mi> </mml:msup> <mml:mo>(</mml:mo> <mml:mi>K</mml:mi> <mml:mo>)</mml:mo> </mml:math> . In particular, we prove that the self-improving property of …