On some properties of multiple conjugate trigonometric series |
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Authors: | D Leladze |
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Institution: | (1) Faculty of Mechanics and Mathematics, I. Javakhishvili Tbilisi State University, 2, University St., 380043 Tbilisi, Republic of Georgia |
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Abstract: | We have obtained an estimate, in terms of partial and mixed moduli, of the continuity of deviation of the Cesáro (C, ) means ( = (1,...,n),i , 1 > –1,
) of the sequence of rectangular partial sums ofn-multiple (n>1) conjugate trigonometric series from then-multiple truncated conjugate function. This estimate implies the result on them
-convergence (1) of (C, ) means (1 > 0,
) provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown that them
-convergence cannot be replaced by ordinary convergence. |
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Keywords: | 42B08 |
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