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Subjects
42-XX Harmonic analysis on Euclidean spaces
42Axx Harmonic analysis in one variable
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series

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Développement en séries trigonométriques des polynômes de M. Léauté

Paul Appell (1897)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Die Theorie der Fourier'schen Integrale und Formeln

Du Bois-Keymond (1871)

Mathematische Annalen

Double sine series with nonnegative coefficients and Lipschitz classes

Vanda Fülöp (2006)

Colloquium Mathematicae

Denote by $f_{s s} (x, y)$ the sum of a double sine series with nonnegative coefficients. We present necessary and sufficient coefficient conditions in order that $f_{s s}$ belongs to the two-dimensional multiplicative Lipschitz class Lip(α,β) for some 0 < α ≤ 1 and 0 < β ≤ 1. Our theorems are extensions of the corresponding theorems by Boas for single sine series.

Currently displaying 1 – 3 of 3

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