Open AccessL1-convergence of double trigonometric series
Author(s) -
Karanvir Singh,
Kanak Modi
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1912759s
Subject(s) - trigonometric series , mathematics , function series , series (stratigraphy) , trigonometric integral , pointwise convergence , trigonometric polynomial , sine , pythagorean trigonometric identity , trigonometric functions , trigonometric substitution , differentiation of trigonometric functions , proofs of trigonometric identities , convergence (economics) , norm (philosophy) , mathematical analysis , trigonometry , power series , polynomial , geometry , paleontology , approx , linear interpolation , computer science , economics , political science , law , bicubic interpolation , biology , operating system , economic growth
In this paper we study the pointwise convergence and convergence in L1-norm of double trigonometric series whose coefficients form a null sequence of bounded variation of order (p,0),(0,p) and (p,p) with the weight (jk)p-1 for some integer p > 1. The double trigonometric series in this paper represents double cosine series, double sine series and double cosine sine series. Our results extend the results of Young [9], Kolmogorov [4] in the sense of single trigonometric series to double trigonometric series and of M?ricz [6,7] in the sense of higher values of p.