This paper deals with the Fourier coefficients of a function of class <mml:math alttext="$L^p $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:mrow></mml:math>. We give a necessary and sufficient condition for function to be of class <mml:math alttext="$L^p $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:mrow></mml:math> for <mml:math alttext="$p$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math> greater than one.

A theorem for Fourier coefficients of a function of class <mml:math alttext="$L^p $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:mrow></mml:math>

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International Journal of Mathematics and Mathematical Sciences

A theorem for Fourier coefficients of a function of class Lp

Abstract

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