Negative order Cesàro means of double Fourier series and bounded generalized variation

Summability of multiple Fourier series of functions of bounded generalized variation

“…Observe that by Theorem 1.4 we have the inclusion n log n # BV ⊂ HBV . Now, for a sequence Λ = {λ n } we denote [12]). We say that the function…”

“…Under what conditions on the sequence Λ = {λ n } the double Fourier series of any function f ∈ CΛ # BV is (C; −α, −β) summable. Theorem 3.2 (U. Goginava [12]). a) Let α, β ∈ (0, 1) , α + β < 1 and f ∈ C n 1−(α+β) # BV .…”

“…Then the double Fourier series of the function f is (C; −α, −β) summable to f * (x, y) in any regular point (x, y). The summability is uniform on any compact K, if f is continuous on the neighborhood of K.In[12] the following problem was considred. Let α, β ∈ (0, 1) , α + β < 1.…”