Cím: | $L\sp 1$-convergence of double Fourier series. |
Szerző: | M\'oricz, Ferenc |
Forrás: | J. Math. Anal. Appl. 186, No.1, 209-236 (1994). |
Nyelv: | English |
Absztrakt: | We prove the convergence in $L\sp 1$-norm of the double Fourier series of an integrable function $f(x,y)$ which is $2\pi$-periodic with respect to $x$ and $y$, with coefficients $a\sb{ij}$ satisfying certain conditions of the Hardy-Karamata kind, and such that $a\sb{jk}\log j\log k\to 0$ as $j,k\to \infty$. We consider separately double cosine, sine, cosine-sine, and complex trigonometric series. |
Letöltés: | | Zentralblatt |