Abstract
The pointwise convergence problem of the rectangular partial sums of a certain type of double trigonometric series is considered, This type of series obeys certain conditions on the finite-order differences of its coefficients. We prove that if the Césaro sums of the double series converge unrestrictedly, then so do its partial sums, It is pointed out that the converse of the last statement may not hold for the same kind of double trigonometric series. As a corollary, it is shown that the double Fourier series of the mentioned type converges unrestrictedly almost everywhere. Generalizations of the above results to the restricted case are also established. These results generalize the theorems of Chen.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
