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Convergence and integrability of double trigonometric series with coefficients of bounded variation
| Content Provider | Semantic Scholar |
|---|---|
| Author | Móricz, Ferenc |
| Copyright Year | 1988 |
| Abstract | We prove that if c(j, k) -. 0 as max(IjI, lkl) -p oo and E E IA1c(j,k) < oo, j=-oo k=-oo then the series c7? _ c(j, k)ei(ij+ky) converges both pointwise for every (x,y) E (T\{0})2 and in the LP(T2)-metric for 0 < p < 1, where T is the one-dimensional torus. Both convergence statements remain valid for the three conjugate series under these same coefficient conditions. |
| Starting Page | 633 |
| Ending Page | 640 |
| Page Count | 8 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-1988-0928995-2 |
| Volume Number | 102 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/1988-102-03/S0002-9939-1988-0928995-2/S0002-9939-1988-0928995-2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-1988-0928995-2 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
