The Journal of the Indian Mathematical Society

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A Note on Functions of p(n)-Λ-Bounded Variation


Affiliations
1 Department of Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara-390002, India
     

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In this note, introducing the class ΛBV (p(n)↑p, φ, [0, 2π] ) (1≤p≤1) of 2π-periodic functions of p(n)-􀀀Λ bounded variation, we prove that it is a convolution Banach algebra with respect to the variation norm. We further show that infact L*ΛBV (p(n)↑p,φ)⊆ ΛBV (p(n)↑p,φ). Finally, we estimate the order of magnitude of Fourier coefficients of functions of the class ΛBV (p(n)↑1,φ).

Keywords

Banach Algebra, Fourier Coefficients, Generalized Wiener Class, Function of ΛBV (p(n)↑∞,φ).
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  • A Note on Functions of p(n)-Λ-Bounded Variation

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Authors

R. G. Vyas
Department of Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara-390002, India

Abstract


In this note, introducing the class ΛBV (p(n)↑p, φ, [0, 2π] ) (1≤p≤1) of 2π-periodic functions of p(n)-􀀀Λ bounded variation, we prove that it is a convolution Banach algebra with respect to the variation norm. We further show that infact L*ΛBV (p(n)↑p,φ)⊆ ΛBV (p(n)↑p,φ). Finally, we estimate the order of magnitude of Fourier coefficients of functions of the class ΛBV (p(n)↑1,φ).

Keywords


Banach Algebra, Fourier Coefficients, Generalized Wiener Class, Function of ΛBV (p(n)↑∞,φ).