(C, 1) Summability of the Differentiated Fourier Series

On the Summability of the Differentiated Fourier Series

Logarithmic Summability of Fourier Series

A set of regular summations logarithmic methods is introduced. This set includes Riesz and Nörlund logarithmic methods as limit cases. The application to logarithmic summability of Fourier series of continuous and integrable functions are given. The kernels of these logarithmic methods for trigonometric system are estimated.

On C 1 - Summability of Series

be any sequence of signs .

On (N, p, q)(E, 1) Summability of Fourier Series

H. K. Nigam and Ajay Sharma Department of Mathematics, Faculty of Engineering & Technology, Mody Institute of Technology and Science (Deemed University), Laxmangarh, Sikar (Rajasthan) 332311, India Correspondence should be addressed to Ajay Sharma, [email protected] Received 7 November 2008; Revised 17 March 2009; Accepted 30 March 2009 Recommended by Hüseyin Bor A new theorem on N...

l1-summability of higher-dimensional Fourier series

It is proved that the maximal operator of the l1-Fejér means of a d-dimensional Fourier series is bounded from the periodic Hardy space Hp(T ) to L p(T ) for all d/(d+1) < p ≤ ∞ and, consequently, is of weak type (1, 1). As a consequence we obtain that the l1-Fejér means of a function f ∈ L1(T ) converge a.e. to f . Moreover, we prove that the l1-Fejér means are uniformly bounded on the spaces ...