On weighted integrability of double sine series. (English) Zbl 1440.42011
Summary: We introduce a new class of double sequences \(D G M(\alpha, \beta, \gamma, r)\) called double general monotone and some new class of weight functions to study the weighted integrability of double sine series. Some results of D. Yu et al. [Anal. Math. 38, No. 2, 83–104 (2012; Zbl 1265.42022)] are also generalized.
MSC:
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
| 42A05 | Trigonometric polynomials, inequalities, extremal problems |
| 42A32 | Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) |
| 40A05 | Convergence and divergence of series and sequences |
| 42B05 | Fourier series and coefficients in several variables |
Keywords:
double sine series; weighted integrability; classes of double sequences; generalized monotonicity; weight functionsCitations:
Zbl 1265.42022References:
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