Two nonequivalent conditions for weight functions
Two nonequivalent conditions for weight functions
A nonnegative function on the real line satisfies the condition <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper A Subscript normal infinity"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">A</mml:mi> </mml:mrow> </mml:mrow> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{{\mathbf {A}}_\infty }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if, given <inline-formula content-type="math/mathml"> <mml:math …