Two-dimensional Waterman classes and u-convergence of Fourier series
- M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
New results on the u-convergence of the double Fourier series of functions from Waterman classes are obtained. It turns out that none of the Waterman classes wider than BV(T{sup 2}) ensures even the uniform boundedness of the u-sums of the double Fourier series of functions in this class. On the other hand, the concept of u(K)-convergence is introduced (the sums are taken over regions that are forbidden to stretch along coordinate axes) and it is proved that for functions f(x,y) belonging to the class {lambda}{sub 1/2}BV(T{sup 2}), where {lambda}{sub a}={l_brace}n{sup 1/2}/(ln(n+1)){sup a}{r_brace}{sub n=1}{sup {infinity}}, the corresponding u(K)-partial sums are uniformly bounded, while if f(x,y) element of {lambda}{sub a}BV(T{sup 2}), where a<1/2, then the double Fourier series of f(x,y) is u(K)-convergent everywhere.
- OSTI ID:
- 21202881
- Journal Information:
- Sbornik. Mathematics, Vol. 190, Issue 7; Other Information: DOI: 10.1070/SM1999v190n07ABEH000414; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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