Basis and regularity properties of ( p , q )-trigonometric functions and the decay of ( p , q )-Fourier coefficients

Author:

Edmunds David E.1,Melkonian Houry2ORCID

Affiliation:

1. Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK

2. Department of Mathematics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

Abstract

The basis and regularity properties of the generalized trigonometric functions sin p , q and cos p , q are investigated. Upper bounds for the Fourier coefficients of these functions are given. Conditions are obtained under which the functions cos p , q generate a basis of every Lebesgue space L r (0,1) with 1 < r < ; when q is the conjugate of p , it is sufficient to require that p ∈[ p 1 , p 2 ], where p 1 <2 and p 2 >2 are calculable numbers. A comparison is made of the speed of decay of the Fourier sine coefficients of a function in Lebesgue and Lorentz sequence spaces with that of the corresponding coefficients with respect to the functions sin p , q . These results sharpen previously known ones.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Reference15 articles.

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2. A remark on certain nonlinear elliptic equations;Ôtani M;Proc. Fac. Sci. Tokai Univ.,1984

3. Lindqvist P. 1993 Some remarkable sine and cosine functions. Helsingin Teknillinen Korkeakoulu. Matematiikan Laitos.

4. Basis properties of eigenfunctions of the 𝑝-Laplacian

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