We adopt here an extended version of the absolute Nevanlinna summability and apply it to study Fourier series of functions of bounded variations. The absolute < < Riesz summability R, n, β₯ , β₯ G 0, which is equivalent to the absolute Cesaro < < summability C, β₯ , is obtainable from the Nevanlinna su
Absolute Euler Summability of Fourier Series
β Scribed by G.D Dikshit
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 169 KB
- Volume
- 220
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
of Denton (Texas) (Eingegangen am 4.6. 1971) ## 1. Definitions Let a, be a giveninfinite series and let A, = il (n) be a positive inonotonic function of n tending t o infinity with n. We write The series z c n , i s said to he summable (R, An, r ) , r 2 0, t o sum s, if A > ( w ) / w ' --+ s, as
The two-dimensional classical Hardy spaces H p (T\\_T) on the bidisc are introduced and it is shown that the maximal operator of the CesaΓ ro means of a distribution is bounded from H p (T\\_T) to L p (T 2 ) ( 3Γ4 (T\\_T), L 1 (T 2 )) where the Hardy space H 1 > (T\\_T) is defined by the hybrid maxi
The d-dimensional classical Hardy spaces H T are introduced and it is shown p that the maximal operator of the Cesaro means of a distribution is bounded from Ε½ that the supremum in the maximal operator is taken over a positive cone. As a consequence we obtain the summability result due to Marcinkie