Integrability of Trigonometric Series with Coefficients Satisfying Certain Conditions

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Integrability of Trigonometric Series with Coefficients Satisfying Certain Conditions

Journal Title: International Journal for Research in Applied Science and Engineering Technology (IJRASET) - Year 2017, Vol 5, Issue 1

Abstract

Let 1  P   and 1  P  P 1, suppose that { an } is a sequence of ,Numbers such that an  Aj or an  A j and        P P n n P P n L n a 1/ 1  2 ( )( ) , then we will prove that 1/ 1 f (x) L(P,) x L P      And   n P n P P P P P f x B P j n L n a x L 1 ( ) , , ( )( ) 1 2 , 1/              & ii)Let { an } be a sequence of numbers such that an  Aj or an  A j . If 1  P   and 1  P  P 1, then a necessary and sufficient condition that 1/ 1 f (x) L(P,) x L P      is that       P n n P P n L(n).

Authors and Affiliations

Dr. Manisha Sharma

Keywords

Integrability of Trigonometric Series Coefficients Satisfying Certain Conditions

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EP ID EP23053
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