𝐿¹-convergence of Fourier series with coefficients of bounded variation

Abstract

It is shown that a Telyakovskii [ <bold>2</bold> ] theorem and its generalization are special cases of a corollary to a theorem of Garrett and Stanojević [ <bold>4</bold> ]. Another theorem of Garrett and Stanojević is generalized for the case of coefficients of bounded variation of order <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m greater-than-or-slanted-equals 1"> <mml:semantics> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo> ⩾ </mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">m \geqslant 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> .