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The ๐ป^{๐‘} classes for ๐›ผ-convex functions

The ๐ป^{๐‘} classes for ๐›ผ-convex functions

Given <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha greater-than 0"> <mml:semantics> <mml:mrow> <mml:mi>ฮฑ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\alpha &gt; 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we determine the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript p"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{H^p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> class to which an <inline-formula โ€ฆ