Almost everywhere convergence of Vilenkin-Fourier series of 𝐻¹ functions
Almost everywhere convergence of Vilenkin-Fourier series of 𝐻¹ functions
In [5] Ladhawala and Pankratz proved that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding="application/x-tex">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is in dyadic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript 1"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{H^1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then any lacunary sequence of partial …