Cím: | Pointwise convergence of multiple trigonometric series. |
Szerző: | Chen, Chang-Pao; Wu, Hui-Chuan; M\'oricz, Ferenc |
Forrás: | J. Math. Anal. Appl. 185, No.3, 629-646 (1994). |
Nyelv: | English |
Absztrakt: | This paper is devoted to the study of pointwise convergence of
the rectangular partial sums of multiple trigonometric series
with coefficients satisfying certain conditions involving finite-order
differences. Three types of such conditions are posed. Convergence
may be understood both in the unrestricted sense and in the restricted
sense. We prove that if the first arithmetic mean of an $n$-fold
trigonometric series of the above type converges, then so does
its rectangular partial sum. As a corollary, we obtain that any
multiple Fourier series of the above type converges restrictedly
almost everywhere. These results extend those of C.-P. Chen,
C.-P. Chen and P.-H. Hsieh, F. M\'oricz, and F. M\'oricz and
D. Waterman. |
Letöltés: | | Zentralblatt |