Subharmonicity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>p</mml:mi></mml:msup></mml:math> for quasiregular harmonic functions, with applications

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